Echo Most Recent Sticky Post in Loop?

If it’s your main loop, you could add this to your function.php:

function custom_pre_get_posts($query) {
    if($query->is_main_query() && /* is sticky conditional tag(sorry I need to check what is that) */) {
        $query->set('posts_per_page', "1");
    }
}
add_action('pre_get_posts', 'custom_pre_get_posts');

Or you can make a new WP_Query instance in the theme file:

<?php 
$onePost = new WP_Query(array(
    'post_type' => // your post type,
    'posts_per_page' => 1,
    'post__in' => get_option('sticky_posts')
));
if($onePost->have_posts()) :
    while(($onePost->have_posts()) :
        $onePost->the_post(); 
?>
// your post HTML as normal
<?php 
    endwhile;
    wp_reset_query();
    endif; 
?>

Please note that if you use the WP_Query then you need to set all parameters you need to custom the post. You could read this in the WP_Query Codex