Functions.php:

	// *** Comments on/off
	
	$wp_customize->add_section( 'display_comments', array(
		'title'		=> 'Comments',
		'priority'	=> 36,
	) );
	
	$wp_customize->add_setting( 'mytheme_comments' );
	
	$wp_customize->add_control( 'mytheme_comments', array(
		'label'   => 'Comments on or off',
		'section' => 'display_comments',
		'type'    => 'select',
		'default' => On,
		'choices' => array(
			'value1' => On,
			'value2' => Off,
			),
	) );

Single.php:

                    <?php $var = get_theme_mod('mytheme_comments');
		       if ($var == 'On') {
			  comments_template();
		       } else if ($var == 'Off') {
		          // Var is Off
		       } else {
		          comments_template();
		       } 
                    ?>