Get the first category name and link in WordPress post's while loop.

the_first_category_name.php

<?php
// Get the 1ast category link
function Chaoz_first_category_link() {
    $cats = get_the_terms(get_the_ID(), 'category');
    $cat  = is_array($cats) ? get_category_link($cats[0]->term_id) : '';
    echo esc_url($cat);
}

// Get the first category link
function Chaoz_first_category_link() {
    $cats = get_the_terms(get_the_ID(), 'category');
    $cat  = is_array($cats) ? get_category_link($cats[0]->term_id) : '';
    echo esc_url($cat);
}