We already went through that one , notice it is a failed treaty<quoted text>
Actually International Space Law does not allow private ownership of the Moon, so it will take some new laws to open up the possibility of individual property rights.
But the idea that humans would be thought of as "aliens" when visiting their own moon is still arguable.
A short and somewhat incomplete overview -- " http://en.wikipedia.org/wiki/Outer_Space_Trea... ;
it was never ratified and the path to this premise is set in motion.
You will probably see the own-age of lunar property in your life.