CLR profiler does not seem to work with the Silverlight CLR. Does another memory profiler exist?
Doesn't seem to be one available yet. However, as recommended in this forum thread, you can convert your Silverlight app to a WPF application and profile that:
There is no tool as of now but as a workaround you can easily create a desktop (WPF) version of your Silverlight client from the same code base and few tweaks (refer Scot's blog for an example on this - http://weblogs.asp.net/scottgu/pages/silverlight-tutorial-part-8-creating-a-digg-desktop-application-using-wpf.aspx) . Once you are done with this you can run any performance profiler that works with WPF.
Not an optimal solution, but it sounds like the best option for now...
Update: Just saw a blog post about XPerf which is a cpu sampler for Silverlight. Not exactly a memory profiler but a good tool for testing the performance of Silverlight apps...