Get First category associated with a post

gistfile1.php

<?php 
$post_categories = wp_get_post_categories( $post->ID );
// get first category id 
$first_cat = get_category($post_categories[0]); 
// get category term info. 
$term_link = get_term_link( $first_cat->slug, $first_cat->taxonomy );
// do what you want with it. 
echo "<a href='".$term_link."'>".$first_cat->name."</a>"; 
?>