It doesn't make any difference, just as you create a winforms app that has a reference to a WCF service, you can add a reference to your WCF service from your ASP.NET project as well.
However, if you want to make a chat like application (generally, any real-time communication with your web users), I recommend taking a look at SignalR.
Update:
If you're insisting on using WCF for implementing this, take a look at this CodeProject article which explains exactly what you're trying to achieve.