Webclient calls to DownloadString cause my app to freeze

will help you You will most likely want to use DownloadStringAsync. Then implement the events on it http://msdn.microsoft.com/en-us/library/system.net.webclient_events(VS.80).aspx DownloadCompleted.
http://msdn.microsoft.com/en-us/library/system.net.webclient.downloadstringasync(VS.80).aspx

I wish this helpful for you Are you using Silverlight? Only the Async version is available in Silverlight. Otherwise, the .NET 4 Framework and below (except 1.x) have the DownloadString() method.
http://msdn.microsoft.com/en-us/library/ms144200.aspx

help you fix your problem You probably want to think about how you are calling the CallGowalla() method. It is probably easier to start calling this method in an async manner. Take a look at some of the examples on this Microsoft KB article. Your CallGowalla() method is equivalent to LongRunningMethod() in those samples.
Running methods asynchronously, perhaps using additional threads, can be problematic in some environments like ASP.NET. It is important to research issues dependent upon your environment. If you are trying to get higher throughput (more calls to Gowalla) then you might want to look into use of the ThreadPool to execute your method without managing threads. The problem with this is that you might exceed the Gowalla API limits very quickly. It would be good if you could provide more detail on why you need to make these calls asynchrously.

Hope this helps The latency was due to a certificate validation timeout. One of the issuer in the chain was not correctly deployed in the client server.

will help you I've found the reason. The developer (me) is an idiot.
Sorry to have wasted your time on this one. When I started stripping down the before and after code to post as a sample I found a Thread.Sleep() in the before code that was there for testing purposes.