Index: src/wp-includes/default-widgets.php
===================================================================
--- src/wp-includes/default-widgets.php	(revision 28807)
+++ src/wp-includes/default-widgets.php	(working copy)
@@ -431,6 +431,8 @@
  */
 class WP_Widget_Calendar extends WP_Widget {
 
+	var $show_id = true;
+
 	public function __construct() {
 		$widget_ops = array('classname' => 'widget_calendar', 'description' => __( 'A calendar of your site’s Posts.') );
 		parent::__construct('calendar', __('Calendar'), $widget_ops);
@@ -445,7 +447,12 @@
 		if ( $title ) {
 			echo $args['before_title'] . $title . $args['after_title'];
 		}
-		echo '<div id="calendar_wrap">';
+		if( $this->show_id ) {
+			echo '<div id="calendar_wrap" class="calendar_wrap">';
+			$this->show_id = false;
+		} else {
+			echo '<div class="calendar_wrap">';
+		}
 		get_calendar();
 		echo '</div>';
 		echo $args['after_widget'];