There is no easy way to get chat embedded in your app. I have chat in my app but its taking me over 2 mouths trying stuff to get it to work. You can make a browser open with chat in it. But its not embed. Use this code.
string sUsername = "USERNAME HERE";
string sUrl = "http://www.twitch.tv/" + sUsername + "/chat";
Process.Start(sUrl);
You app is coming alone good.
You can read here Twitch chat wont load in webbrowser control vb.net to see what I used. More info here https://www.google.com/#q=geckofx%20c%23 Or get someone to add it or give you all the code and files you will need for it but that kinda stuff aint free.