Get random post which has featured image

This should do it:

<?php 

	$args = array(
		'post_type' => 'post',
		'orderby' => 'rand',
		'posts_per_page' => 1,
		'meta_key' => '_thumbnail_id'
	);
	$query = new WP_Query($args);

	while ( $query->have_posts() ) { $query->the_post();
		//do stuff here (the_title() or the_content(), etc)
	} wp_reset_postdata(); 

?>