diff --git a/chalice/cli/filewatch/stat.py b/chalice/cli/filewatch/stat.py
index f4a987621..180fe977a 100644
--- a/chalice/cli/filewatch/stat.py
+++ b/chalice/cli/filewatch/stat.py
@@ -56,7 +56,12 @@ def _seed_mtime_cache(self, root_dir):
         for rootdir, _, filenames in self._osutils.walk(root_dir):
             for filename in filenames:
                 path = self._osutils.joinpath(rootdir, filename)
-                self._mtime_cache[path] = self._osutils.mtime(path)
+                try:
+                    self._mtime_cache[path] = self._osutils.mtime(path)
+                except (OSError, IOError):
+                    # This can happen with broken symlinks or files that
+                    # disappear between walk() and mtime().
+                    LOGGER.debug("Unable to stat file: %s, skipping.", path)
 
     def _single_pass_poll(self, root_dir, callback):
         # type: (str, Callable[[], None]) -> None
diff --git a/tests/unit/cli/filewatch/test_stat.py b/tests/unit/cli/filewatch/test_stat.py
index 28015cfec..fb9a4e660 100644
--- a/tests/unit/cli/filewatch/test_stat.py
+++ b/tests/unit/cli/filewatch/test_stat.py
@@ -38,3 +38,42 @@ def callback(*args, **kwargs):
         time.sleep(0.2)
     else:
         raise AssertionError("Expected callback to be invoked but was not.")
+
+
+class FakeOSUtilsWithBrokenSymlink(object):
+    """Simulates a broken symlink that fails os.stat during initial cache seed.
+
+    This can happen with symlinks pointing to non-existent files, such as
+    Emacs lock files (.#app.py) or other temporary symlinks.
+    """
+    def __init__(self):
+        self.scan_count = 0
+
+    def walk(self, rootdir):
+        self.scan_count += 1
+        yield 'rootdir', [], ['broken-symlink', 'good-file']
+
+    def joinpath(self, *parts):
+        return os.path.join(*parts)
+
+    def mtime(self, path):
+        if path.endswith('broken-symlink'):
+            raise FileNotFoundError("No such file or directory")
+        return 1
+
+
+def test_can_handle_broken_symlink_during_initial_scan():
+    """Test that broken symlinks during initial cache seeding are handled.
+
+    This is a regression test for issue #997 where symlinks to non-existent
+    files (like Emacs .#app.py files) would crash the file watcher during
+    the initial _seed_mtime_cache call.
+    """
+    osutils = FakeOSUtilsWithBrokenSymlink()
+    watcher = stat.StatFileWatcher(osutils)
+    # This should not raise an exception
+    watcher._seed_mtime_cache('rootdir')
+    # The good file should be in the cache, the broken symlink should not
+    assert len(watcher._mtime_cache) == 1
+    assert 'rootdir/good-file' in watcher._mtime_cache or \
+           os.path.join('rootdir', 'good-file') in watcher._mtime_cache