How to show only one category in breadcrumb navigation

get_the_category() function used to retrieve categories array of a post, and array_shift() function used to get the first item of an array.

You possibly need this –

function ux_breadcrumbs() {
    if (!is_home()) {
        echo '<a href="';
        echo get_option('home');
        echo '">';
        bloginfo('name');
        echo "</a> » ";
        if (is_category() || is_single() )
        {
            if( is_category() )
            {
                single_term_title();
            }
            elseif (is_single() )
            {
                echo " » ";
                $cats = get_the_category( get_the_ID() );
                $cat = array_shift($cats);
                echo '<a href="' . esc_url( get_category_link( $cat->term_id ) ) . '" title="' . esc_attr( sprintf( __( "View all posts in %s" ), $cat->name ) ) . '">'. $cat->name .'</a>';
                echo "  ";
                the_title();
            }
        } elseif (is_page()) {
            echo the_title();
        }
    }
}