The Mailchimp WordPress plugin List Subscribe Form doesn’t have Google Analytics tracking built-in so you must write custom JavaScript. Note in mailchimp.js that the subscription form is reset upon successful submission, so you can hook into that event to trigger GA’s tracking code. Assuming you’ve added Google Analytics property code via a WordPress plugin or theme, and setup the goal’s event rules, use this example jQuery:

$(function() {
    $('#mc_signup_form').bind('reset', function() {
        if($('#mc_signup_form .mc_success_msg').length) {
            if('undefined' !== typeof _gaq) {
                // using ga.js
                _gaq.push(['_trackEvent', 'mailchimp', 'subscribe']);
            } else if ('function' === typeof ga) {
                // using analytics.js
                ga('send', 'event', 'mailchimp', 'subscribe');