Could China Make claims to the Moon that could trigger a new space race?

Glenn Harlan Reynolds (Instapundit) wrote in USA Today that he hopes China makes territorial claims to the moon to start a gold rush for space resources.
On Saturday, a Chinese lunar probe made the first soft landing anyone’s made on the moon since 1976.
The Chang’e-3 probe means that China is one of only three countries — joining the United States and the old Soviet Union — to accomplish such a feat. The probe includes an unmanned rover named Yutu that will spend several months exploring "geological structure and surface substances and looking for natural resources.” But will China try to claim the ground it explores? Possibly.
October Sky author Homer Hickam was more excited. He wondered on Twitter if China might want to make a territorial claim on the moon, noting that the area the lander is exploring may contain an abundance of Helium-3, a potentially valuable fusion energy fuel that is found only on the moon.
According to former astronaut/geologist Harrison Schmitt, China "has made no secret" of its interest in Helium-3. Schmitt observes, "I would assume that this mission is both a geopolitical statement and a test of some hardware and software related to mining and processing of the lunar regolith."
Companies can make claims and countries can withdraw from the Outer Space Treaty with one year’s notice
The 1967 Outer Space Treaty provides that "outer space, including the moon and other celestial bodies, is not subject to national appropriation by claim of sovereignty, by means of use or occupation, or by any other means." But that’s not much of a barrier.
First, the treaty only prohibits "national appropriation." If a Chinese company, instead of the Chinese government, were to stake a claim, it wouldn’t apply. And, at any rate, China — which didn’t even join the treaty until 1983 — can, like any other nation, withdraw at any time. All that’s required under the treaty is to give a year’s notice.