After searching online for some time I was unable to find a real answer.
It it possible to start an application (i.e. Chrome) in a way that it always goes fullscreen?
Just leave the app in full screen mode when you quit the application. As long as it's using Lion's full screen library (and not some hack of its own), the next time you start the app it will start back up in full screen mode.
Just tested this with Safari and Sparrow and they both restarted in full screen mode. Chrome 15.0.874.106, however, did not. I don't think Chrome's full screen support on Lion is quite right, it might not be using Lion's full screen window methods in the ways necessary to have it resume in full screen mode.
The best solution I can find is the shortcut "alt+⌘+F" for Full Screen mode.
Find the shortcut for the one you want in the View menu.