AJAX is not officially supported yet - the last I heard it was on
"maybe" list for SP1.

Ajax .NET application can currently run under sharepoint (though
probably not oficially supported). We run custom app. under
Sharepoint, using ajax  and AJAX Control Toolkit. There should be a
couple of Ajax-specific changes in web.config. Here is a couple of
resources:

sharepoint.microsoft.com/.../Post.aspx?
ID=3 -integrating ASP.NET ajax apps with sharepoint

http://www.codeplex.com/sharepointajax -this is a Sharepoint Ajax
Toolkit -will help with ajax in webparts

weblogs.asp.net/.../using-the-ajax-control-
toolkit-in-sharepoint.aspx -Using the AJAX Control Toolkit in
SharePoint