Use http://tmi.twitch.tv/group/user/CHANNEL_NAME/chatters I don’t believe there’s official API documentation for it but most people I’ve spoken to seem to use this method of getting people in chat. Though I can not speak as to whether or not it’s allowed.
The data is JSON so depending on what language you’re using, find a way to parse it. In Javascript, you’d use JSON.parse(stringData) to convert what’s on that page to a Javascript object.