diff --git a/tests/test_widget_visibility.py b/tests/test_widget_visibility.py
new file mode 100644
index 0000000000..c625771ff0
--- /dev/null
+++ b/tests/test_widget_visibility.py
@@ -0,0 +1,34 @@
+from textual.app import App, ComposeResult
+from textual.widgets import Label
+
+
+async def test_hide() -> None:
+    """Check that setting visibility produces Hide messages."""
+    # https://github.com/Textualize/textual/issues/3460
+    visibility: list[bool] = []
+
+    class ShowHideLabel(Label):
+        def on_show(self) -> None:
+            visibility.append(True)
+
+        def on_hide(self) -> None:
+            visibility.append(False)
+
+    class ShowHideApp(App[None]):
+        BINDINGS = [("space", "toggle_label")]
+
+        def compose(self) -> ComposeResult:
+            yield ShowHideLabel("Here I am")
+
+        def action_toggle_label(self) -> None:
+            self.query_one(ShowHideLabel).visible = not self.query_one(
+                ShowHideLabel
+            ).visible
+
+    app = ShowHideApp()
+    async with app.run_test() as pilot:
+        assert visibility == [True]
+        await pilot.press("space")
+        assert visibility == [True, False]
+        await pilot.press("space")
+        assert visibility == [True, False, True]