Index: wp-includes/post-template.php
===================================================================
--- wp-includes/post-template.php	(revision 22085)
+++ wp-includes/post-template.php	(working copy)
@@ -500,8 +500,10 @@
 	if ( is_user_logged_in() )
 		$classes[] = 'logged-in';
 
-	if ( is_admin_bar_showing() )
+	if ( is_admin_bar_showing() ) {
 		$classes[] = 'admin-bar';
+		$classes[] = 'no-customize-support';
+	}
 
 	if ( get_theme_mod( 'background_color' ) || get_background_image() )
 		$classes[] = 'custom-background';