Don't do things like this.
If you need to maintain data between pages, use Session state. That's what it's for. You should remember that you get a new instance of your page class on every request. Do not use statics to keep changing data around for subsequent requests. You will probably get into trouble with multiple requests updating the data at the same time.
You can't do things like this with ASP.NET!
You seem to be treating this as though it were a desktop program - as though your class instance and all state will still be there for you next time you execute a method on the page. That's not true - when the request is complete, your page will be Disposed. Nothing about the page will remain valid.
In particular, if the callback doesn't happen before the request ends, then the callback method had better not reference anything having to do with the request, like your page. That's because the callback might fire after the request is already over! The state is corrupt or worse.
Unless you are going to have the page wait for the callback, you'd really better not use them in your pages. Instead, create a separate Windows Service or something and have it issue the requests and await the callback. The page can then use Ajax or something to ask if the request is complete, and to get the response once complete.
If you think you heard me say to call back to an ASP.NET page, then you misunderstood.
Create a Windows Service. Your Windows Service will host a WCF service that the ASP.NET application will talk to. The WCF Service will keep track of things like who's joined a chat, who's typing, etc.
The web application cannot be notified when something interesting happens. Instead, the web application will have to poll the WCF service, asking if anything interesting has happened. When something happens, the WCF service will pass the "something" back to the ASP.NET application (or possibly, back to the page, called by AJAX).
I misspoke earlier. You simply cannot use a callback contract at all in this situation. It's not like the web pages are like a desktop application, one per user, waiting to be notified. They're more like a desktop application where, when the user makes a request, you take his PC and give him a new one just like it, before the response arrives.