Laravel Echo Not Listening

At least, that's what I assume is happening. I have been following this tutorial: https://pusher.com/tutorials/chat-laravel/ and everything works great up until I try to make it realtime. At this point, I can send and receive messages, but have to refresh to get them. Any help is appreciated.

bootstrap.js

window._ = require('lodash');

/**
 * We'll load jQuery and the Bootstrap jQuery plugin which provides support
 * for JavaScript based Bootstrap features such as modals and tabs. This
 * code may be modified to fit the specific needs of your application.
 */

try {
    window.$ = window.jQuery = require('jquery');

    require('bootstrap-sass');
} catch (e) {}

/**
 * We'll load the axios HTTP library which allows us to easily issue requests
 * to our Laravel back-end. This library automatically handles sending the
 * CSRF token as a header based on the value of the "XSRF" token cookie.
 */

window.axios = require('axios');

window.axios.defaults.headers.common['X-Requested-With'] = 'XMLHttpRequest';

/**
 * Next we will register the CSRF Token as a common header with Axios so that
 * all outgoing HTTP requests automatically have it attached. This is just
 * a simple convenience so we don't have to attach every token manually.
 */

let token = document.head.querySelector('meta[name="csrf-token"]');

if (token) {
    window.axios.defaults.headers.common['X-CSRF-TOKEN'] = token.content;
} else {
    console.error('CSRF token not found: https://laravel.com/docs/csrf#csrf-x-csrf-token');
}

/**
 * Echo exposes an expressive API for subscribing to channels and listening
 * for events that are broadcast by Laravel. Echo and event broadcasting
 * allows your team to easily build robust real-time web applications.
 */

 import Echo from 'laravel-echo'

 window.Pusher = require('pusher-js');
 Pusher.logToConsole = true;

 window.Echo = new Echo({
     broadcaster: 'pusher',
     key: 'MyCorrectPusherKey',
     cluster: 'mt1',
     encrypted: true
 });

app.js

/**
 * First we will load all of this project's JavaScript dependencies which
 * includes Vue and other libraries. It is a great starting point when
 * building robust, powerful web applications using Vue and Laravel.
 */

require('./bootstrap');

window.Vue = require('vue');

/**
 * Next, we will create a fresh Vue application instance and attach it to
 * the page. Then, you may begin adding components to this application
 * or customize the JavaScript scaffolding to fit your unique needs.
 */

Vue.component('example', require('./components/Example.vue'));
Vue.component('chat-messages', require('./components/ChatMessages.vue'));
Vue.component('chat-form', require('./components/ChatForm.vue'));

const app = new Vue({
    el: '#app',

    data: {
        chat_messages: []
    },

    created() {
        this.fetchChatMessages();
      Echo.private('chat')
        .listen('ChatMessageSent', (e) => {
          this.chat_messages.push({
            message: e.message.body,
            user: e.user
          });
        });
    },

    methods: {
        fetchChatMessages() {
            axios.get('/chitterings/chat/messages').then(response => {
                this.chat_messages = response.data;
            });
        },

        addChatMessage(message) {
            this.chat_messages.push(message);

            axios.post('/chitterings/chat/send', message).then(response => {
              console.log(response.data);
            });
        }
    }
});

ChatMessageSent.php

<?php

namespace App\Events;

use App\Models\Chat;
use App\Models\User;
use Illuminate\Broadcasting\Channel;
use Illuminate\Queue\SerializesModels;
use Illuminate\Broadcasting\PrivateChannel;
use Illuminate\Broadcasting\PresenceChannel;
use Illuminate\Foundation\Events\Dispatchable;
use Illuminate\Broadcasting\InteractsWithSockets;
use Illuminate\Contracts\Broadcasting\ShouldBroadcastNow;

class ChatMessageSent implements ShouldBroadcastNow
{
    use Dispatchable, InteractsWithSockets, SerializesModels;

    /**
     * User that sent the message
     *
     * @var User
     */
    public $user;

    /**
     * Message details
     *
     * @var Message
     */
    public $message;

    /**
     * Create a new event instance.
     *
     * @return void
     */
    public function __construct(User $user, Chat $message)
    {
        $this->user = $user;
        $this->message = $message;
    }

    /**
     * Get the channels the event should broadcast on.
     *
     * @return Channel|array
     */
    public function broadcastOn()
    {
        return new PrivateChannel('chat');
    }

}

I can see the payload for the event in my debug console on pusher, but no subscription or occupation, etc.