diff --git a/io/Makefile b/io/Makefile
index d9a1da4566..fe2f8c5065 100644
--- a/io/Makefile
+++ b/io/Makefile
@@ -74,7 +74,7 @@ tests		:= test-utime test-stat test-stat2 test-lfs tst-getcwd \
 		   tst-posix_fallocate tst-posix_fallocate64 \
 		   tst-fts tst-fts-lfs tst-open-tmpfile \
 		   tst-copy_file_range tst-getcwd-abspath tst-lockf \
-		   tst-ftw-lnk
+		   tst-ftw-lnk tst-lchmod
 
 # Likewise for statx, but we do not need static linking here.
 tests-internal += tst-statx
diff --git a/io/tst-lchmod.c b/io/tst-lchmod.c
new file mode 100644
index 0000000000..73e45549af
--- /dev/null
+++ b/io/tst-lchmod.c
@@ -0,0 +1,314 @@
+/* Tests for lchmod and fchmodat with AT_SYMLINK_NOFOLLOW.
+   Copyright (C) 2020 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <https://www.gnu.org/licenses/>.  */
+
+#include <array_length.h>
+#include <errno.h>
+#include <fcntl.h>
+#include <stdbool.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <support/check.h>
+#include <support/descriptors.h>
+#include <support/namespace.h>
+#include <support/support.h>
+#include <support/temp_file.h>
+#include <support/xunistd.h>
+#include <unistd.h>
+
+#if __has_include (<sys/mount.h>)
+# include <sys/mount.h>
+#endif
+
+/* Array of file descriptors.  */
+#define DYNARRAY_STRUCT fd_list
+#define DYNARRAY_ELEMENT int
+#define DYNARRAY_INITIAL_SIZE 0
+#define DYNARRAY_PREFIX fd_list_
+#include <malloc/dynarray-skeleton.c>
+
+static int
+fchmodat_with_lchmod (int fd, const char *path, mode_t mode, int flags)
+{
+  TEST_COMPARE (fd, AT_FDCWD);
+  if (flags == 0)
+    return chmod (path, mode);
+  else
+    {
+      TEST_COMPARE (flags, AT_SYMLINK_NOFOLLOW);
+      return lchmod (path, mode);
+    }
+}
+
+/* Chose the appropriate path to pass as the path argument to the *at
+   functions.  */
+static const char *
+select_path (bool do_relative_path, const char *full_path, const char *relative_path)
+{
+  if (do_relative_path)
+    return relative_path;
+  else
+    return full_path;
+}
+
+static void
+test_1 (bool do_relative_path, int (*chmod_func) (int fd, const char *, mode_t, int))
+{
+  char *tempdir = support_create_temp_directory ("tst-lchmod-");
+
+  char *path_dangling = xasprintf ("%s/dangling", tempdir);
+  char *path_file = xasprintf ("%s/file", tempdir);
+  char *path_loop = xasprintf ("%s/loop", tempdir);
+  char *path_missing = xasprintf ("%s/missing", tempdir);
+  char *path_to_file = xasprintf ("%s/to-file", tempdir);
+
+  int fd;
+  if (do_relative_path)
+    fd = xopen (tempdir, O_DIRECTORY | O_RDONLY, 0);
+  else
+    fd = AT_FDCWD;
+
+  add_temp_file (path_dangling);
+  add_temp_file (path_loop);
+  add_temp_file (path_file);
+  add_temp_file (path_to_file);
+
+  support_write_file_string (path_file, "");
+  xsymlink ("file", path_to_file);
+  xsymlink ("loop", path_loop);
+  xsymlink ("target-does-not-exist", path_dangling);
+
+  /* Check that the modes do not collide with what we will use in the
+     test.  */
+  struct stat64 st;
+  xstat (path_file, &st);
+  TEST_VERIFY ((st.st_mode & 0777) != 1);
+  xlstat (path_to_file, &st);
+  TEST_VERIFY ((st.st_mode & 0777) != 2);
+  mode_t original_symlink_mode = st.st_mode;
+
+  /* Set to true if AT_SYMLINK_NOFOLLOW is supported.  */
+  bool nofollow;
+
+  /* We should be able to change the mode of a file, including through
+     the symbolic link to-file.  */
+  const char *arg = select_path (do_relative_path, path_file, "file");
+  TEST_COMPARE (chmod_func (fd, arg, 1, 0), 0);
+  xstat (path_file, &st);
+  TEST_COMPARE (st.st_mode & 0777, 1);
+  int ret = chmod_func (fd, path_file, 2, AT_SYMLINK_NOFOLLOW);
+  if (ret == 0)
+    {
+      printf ("info: AT_SYMLINK_NOFOLLOW support in %s\n", tempdir);
+      nofollow = true;
+    }
+  else
+    {
+      printf ("info: no AT_SYMLINK_NOFOLLOW support in %s\n", tempdir);
+      nofollow = false;
+
+      /* Set up things for the code below.  */
+      TEST_COMPARE (chmod_func (fd, path_file, 2, 0), 0);
+    }
+  xstat (path_file, &st);
+  TEST_COMPARE (st.st_mode & 0777, 2);
+  arg = select_path (do_relative_path, path_to_file, "to-file");
+  TEST_COMPARE (chmod_func (fd, path_to_file, 1, 0), 0);
+  xstat (path_file, &st);
+  TEST_COMPARE (st.st_mode & 0777, 1);
+  xlstat (path_to_file, &st);
+  TEST_COMPARE (original_symlink_mode, st.st_mode);
+
+  /* Changing the mode of a symbolic link may fail.  */
+  arg = select_path (do_relative_path, path_to_file, "to-file");
+  ret = chmod_func (fd, arg, 2, AT_SYMLINK_NOFOLLOW);
+  if (nofollow)
+    {
+      TEST_COMPARE (ret, 0);
+
+      /* The mode of the link changed.  */
+      xlstat (path_to_file, &st);
+      TEST_COMPARE (st.st_mode & 0777, 2);
+
+      /* But the mode of the file is unchanged.  */
+      xstat (path_file, &st);
+      TEST_COMPARE (st.st_mode & 0777, 1);
+
+    }
+  else
+    {
+      TEST_COMPARE (ret, -1);
+      TEST_COMPARE (errno, EOPNOTSUPP);
+
+      /* The modes should remain unchanged.  */
+      xstat (path_file, &st);
+      TEST_COMPARE (st.st_mode & 0777, 1);
+      xlstat (path_to_file, &st);
+      TEST_COMPARE (original_symlink_mode, st.st_mode);
+    }
+
+  /* If we have NOFOLLOW support, we should be able to change the mode
+     of a dangling symbolic link or a symbolic link loop.  */
+  const char *paths[] = { path_dangling, path_loop };
+  for (size_t i = 0; i < array_length (paths); ++i)
+    {
+      const char *path = paths[i];
+      const char *filename = strrchr (path, '/');
+      TEST_VERIFY_EXIT (filename != NULL);
+      ++filename;
+      mode_t new_mode = 010 + i;
+
+      xlstat (path, &st);
+      TEST_VERIFY ((st.st_mode & 0777) != new_mode);
+      original_symlink_mode = st.st_mode;
+      arg = select_path (do_relative_path, path, filename);
+      ret = chmod_func (fd, arg, new_mode, AT_SYMLINK_NOFOLLOW);
+      if (nofollow)
+        {
+          TEST_COMPARE (ret, 0);
+          xlstat (path, &st);
+          TEST_COMPARE (st.st_mode & 0777, new_mode);
+        }
+      else /* !nofollow.  */
+        {
+          TEST_COMPARE (ret, -1);
+          TEST_COMPARE (errno, EOPNOTSUPP);
+          xlstat (path, &st);
+          TEST_COMPARE (st.st_mode, original_symlink_mode);
+        }
+    }
+
+   /* A missing file should always result in ENOENT.  The presence of
+      /proc does not matter.  */
+   arg = select_path (do_relative_path, path_missing, "missing");
+   TEST_COMPARE (chmod_func (fd, arg, 020, 0), -1);
+   TEST_COMPARE (errno, ENOENT);
+   TEST_COMPARE (chmod_func (fd, arg, 020, AT_SYMLINK_NOFOLLOW), -1);
+   TEST_COMPARE (errno, ENOENT);
+
+   /* Test without available file descriptors.  */
+   {
+     struct fd_list fd_list;
+     fd_list_init (&fd_list);
+     while (true)
+       {
+         int ret = dup (STDOUT_FILENO);
+         if (ret == -1)
+           {
+             if (errno == ENFILE || errno == EMFILE)
+               break;
+             FAIL_EXIT1 ("dup: %m");
+           }
+         fd_list_add (&fd_list, ret);
+         TEST_VERIFY_EXIT (!fd_list_has_failed (&fd_list));
+       }
+     /* Without AT_SYMLINK_NOFOLLOW, changing the permissions should
+        work as before.  */
+     arg = select_path (do_relative_path, path_file, "file");
+     TEST_COMPARE (chmod_func (fd, arg, 3, 0), 0);
+     xstat (path_file, &st);
+     TEST_COMPARE (st.st_mode & 0777, 3);
+     /* But with AT_SYMLINK_NOFOLLOW, even if we originally had
+        support, we may have lost it.  */
+     ret = chmod_func (fd, arg, 2, AT_SYMLINK_NOFOLLOW);
+     if (ret == 0)
+       {
+         xstat (path_file, &st);
+         TEST_COMPARE (st.st_mode & 0777, 2);
+       }
+     else
+       {
+         TEST_COMPARE (ret, -1);
+         /* The error code from the openat fallback leaks out.  */
+         if (errno != ENFILE && errno != EMFILE)
+           TEST_COMPARE (errno, EOPNOTSUPP);
+       }
+     xstat (path_file, &st);
+     TEST_COMPARE (st.st_mode & 0777, 3);
+
+     /* Close the descriptors.  */
+     for (int *pfd = fd_list_begin (&fd_list); pfd < fd_list_end (&fd_list);
+          ++pfd)
+       xclose (*pfd);
+     fd_list_free (&fd_list);
+   }
+
+   if (do_relative_path)
+    xclose (fd);
+
+   free (path_dangling);
+   free (path_file);
+   free (path_loop);
+   free (path_missing);
+   free (path_to_file);
+
+   free (tempdir);
+}
+
+static void
+test_3 (void)
+{
+  puts ("info: testing lchmod");
+  test_1 (false, fchmodat_with_lchmod);
+  puts ("info: testing fchmodat with AT_FDCWD");
+  test_1 (false, fchmodat);
+  puts ("info: testing fchmodat with relative path");
+  test_1 (true, fchmodat);
+}
+
+static int
+do_test (void)
+{
+  struct support_descriptors *descriptors = support_descriptors_list ();
+
+  /* Run the three tests in the default environment.  */
+  test_3 ();
+
+  /* Try to set up a /proc-less environment and re-test.  */
+#if __has_include (<sys/mount.h>)
+  if (!support_become_root ())
+    puts ("warning: could not obtain root-like privileges");
+  if (!support_enter_mount_namespace ())
+    puts ("warning: could enter a mount namespace");
+  else
+    {
+      /* Attempt to mount an empty directory over /proc.  */
+      char *tempdir = support_create_temp_directory ("tst-lchmod-");
+      bool proc_emptied
+        = mount (tempdir, "/proc", "none", MS_BIND, NULL) == 0;
+      if (!proc_emptied)
+        printf ("warning: bind-mounting /proc failed: %m");
+      free (tempdir);
+
+      puts ("info: re-running tests (after trying to empty /proc)");
+      test_3 ();
+
+      if (proc_emptied)
+        /* Reveal the original /proc, which is needed by the
+           descriptors check below.  */
+        TEST_COMPARE (umount ("/proc"), 0);
+    }
+#endif /* <sys/mount.h>.  */
+
+  support_descriptors_check (descriptors);
+  support_descriptors_free (descriptors);
+
+  return 0;
+}
+
+#include <support/test-driver.c>
