Most likely, Beijing wouldn't try to claim the entire moon, just part of it. For one thing, the cost of demonstrating complete occupation would simply be too high. The moon's surface is, after all, 14.6 million square miles. Second, leaving some of the moon's surface for other powers to claim would legitimize the Chinese annexation.
Would a Chinese moon claim even be legal? At the moment, no, but international law would provide only the flimsiest of barriers. Although the 1967 space treaty asserts common ownership of the entire universe beyond Earth's atmosphere, it also permits signatory states to withdraw from its terms with only a year's notice. And there's no law governing whether you can fly a rocket to the moon and land a ship there.
After renouncing the treaty, Beijing could annex regions of the moon and justify its actions with two arguments: First, in allowing states to withdraw, the treaty implicitly recognizes the possibility of claiming sovereign extraterrestrial territory. Second, after withdrawing from the treaty, China could declare any annexed lunar land terra nullius -- territory belonging to no one and therefore subject to national claims; Article 70 of the 1969 Vienna Convention on the Law of Treaties says that states renouncing or withdrawing from multilateral treaties are released "from any obligation further to perform" the terms of the treaty. Besides, most international law on the question of sovereignty claims defers to self-determination -- the wishes of the inhabitants. Since, as far as we know, there are no inhabitants on the moon, this doesn't apply.
By establishing a permanent moon base, China would also satisfy an important criterion for sovereignty. In the 19th and early 20th centuries, the United States and Britain claimed territorial sovereignty on numerous uninhabited small islands in the Pacific by performing formal rituals such as flag-raising ceremonies. However, in situations in which both the United States and Britain claimed sovereignty, the establishment of a handful of settlers proved a convincing argument. Putting a few dozen people on the moon in permanent rotation would be a lot more legally compelling than simply planting a flag.
International legal norms might even encourage China to assert territorial sovereignty over its lunar lands. If the moon's riches are as vast as many have asserted, Beijing might want to claim sovereignty so that private investors would be willing to develop the region around its moon base. Otherwise, an anarchic scramble for lunar resources, with no legal institutions set up to arbitrate disputes or back up property claims, could result.
This line of argument might seem a lot more Popular Science than Foreign Policy. To most of us, the moon appears impossibly distant and forbiddingly hostile. But remember that Alaska and Australia were no less distant and hostile when Russia and Britain claimed them back in the 18th and 19th centuries. Both territories seemed like wastelands -- until new technologies turned them into economic engines. Russia later exchanged Alaska for cash and warm relations with the United States. In Australia, Britain created a strong ally, molded in its own image, halfway around the world.
So let's not write off a Chinese moon colony as sheer fantasy. Unless steps are taken now to stop it, our children might someday look up to the night sky and really see a red moon rising.