If you're trying to tackle this challenge with jQuery's $.getJSON() method, chances are you'll get an error message concerning Cross-Origin Resource Sharing (CORS).

The easiest way to resolve this is to use jQuery's JSONP capabilities. From the Twitch API's readme page:

All API methods support JSON-P by providing a callback parameter with the request.

Also the jQuery documentation states:

If the URL includes the string "callback=?" (or similar, as defined by the server-side API), the request is treated as JSONP instead.

Here's an example call to fetch Free Code Camp's Twitch channel data:

$.getJSON('https://api.twitch.tv/kraken/streams/freecodecamp?callback=?', function(data) {
  console.log(data);
});

JSONP is considered insecure according to Wikipedia, but should be sufficient for our purposes. For a detailed discussion on Twitch's CORS restriction, please read issue #133 on the Twitch-API repository.