My apologies for overlooking that this is Chrome specific, and yes you are right it would fail in IE as well.
It may be a proxy interference problem. In order for us to automate Silverlight applications in Chrome we start up our own HTTP proxy process and automatically change the proxy settings of the machine to point to our proxy. If Chrome is not recognizing the change in proxy settings, or a third party anti-virus product is interfering, then we won't be able to inject our automation hooks into the Silverlight application.
Can you investigate this possibility?