Get the first category of a post.

wp_get_first_category.php

<?php
/**
 *  Get the first category of a post.
 *
 *  @param   int    $id  The id of a post
 *  @param   int    $id  The field value to return
 *  @return  mixed       The category object or single field
 */
function wp_get_first_category( $id=null, $field='all' ) {
    // Check if only a field value was supplied
    if ( $id ) {
        if ( ! is_numeric( $id ) ) {
            global $post;
            $field = $id;
            $id = $post->ID;
        }
    } else {
        global $post;
        $id = $post->ID;
    }

    // Get all the post's categories
    $categories = get_the_category( $id );

    // Check if there are any categories, if so get the first
    if ( empty( $categories ) ) {
        return false;
    } else if ( isset( $categories[0] ) ) {
        $cat = array_shift( $categories );
    } else {
        $cat = $categories;
    }

    // Check if we should be returning a single field, or the whole object
    if ( $field == 'all' ) {
        return $cat;
    } else {
        return $cat->$field;
    }
}