ASP.NET is a server-side language. The client (a browser I am guessing) doesn't run anything other than JavaScript at the moment.
If you are familiar with C#, then you can use ASP.NET with C# on the backend server. For a chat application check the sample SignalR app in the getting started guide. For tic tac toe, you probably can code the whole thing on the client side using JavaScript. Unless if you want multiple players for one tic tac toe game then you can use a SignalR component to communicate between them.