Sooner or later, when building Silverlight apps that talk to SharePoint 2010 Client Object Model, you will run into this problem. You’ll try and access ClientContext.Current, and for some mysterious reason, it will be null!
Well, mystery solved. What you need to do is, you need to pass the current SharePoint site URL to the Client Object Model as an InitParam. In short, in your Silverlight Object Tag, add the following:
1: "<param name=\"initParams\" value=\"MS.SP.url=" + SPContext.Current.Site.Url + "\" />"
(The above is shown as code-behind code, because that is where you’d have to add that).
By doing so, the Client Object model can now get access to ClientContext.Current.
Happy SharePointing! w00t!