If you haven't heard about the Google App Engine then you should check it out: http://code.google.com/appengine. If you have heard about it then you know that it initially only supports apps written in Python. Google does plan to support other languages and one of the first ones requested was Groovy! In fact the first issue on their issue list is "Add Java and Groovy support".
You can add your support by going to their issue list (http://code.google.com/p/googleappengine/issues/list) and giving that issue a star. You can also add a comment but it's the number of stars that moves an issue to the top of the list. Even though the Java/Groovy request is the first one entered (id = 1) it is currently ranking 5th in stars. Slightly behind Ruby and a good deal behind Perl. This is a great opportunity to be a squeaky wheel. So head on over to the list and give Groovy a star!