Well, the Chinese could try to claim the moon. But I doubt they will have much success in the long run. If the people on the Moon really wanted independence, there is little that nations on Earth could do, because enforcing authority over an unwilling populace becomes expensive.

Antarctica is covered by several treaties that say various nations will give up territorial claims -- at one point the UK, Australia, New Zealand, and Argentina were all saying they had claims to territory. In 2001 the US and Russia reserved the right to make claims and not recognize others claims. The CIA world fact book lists the following: Argentina, Australia, Chile, France, New Zealand, Norway, and the UK.

The Moon could be administered in a similar way, at least initially.