Wild idea, and it sounds impossible to me even typing it, but I shall...
What about having two windows/forms open, one transparent for the drop shadow, the other opaque, and tie the position of the two windows/forms to each other, so you get the same kind of effect?
I'll go and hide now...
Even wilder idea: use the system chrome.
I don't like any application that doesn't use the system chrome. This includes e.g. WLM and older versions of WMP (where I always turn the chrome on first thing). I also greatly dislike that all of the Silverlight 4 OOB apps I've seen so far use
a custom chrome (I'm not sure if they can have the default chrome or not).
If I used Twitter (which I don't), I would likely not use this app because of its use of a custom window chrome.