I know it's rare, but I think xeno may be right. (Just joking around, xeno... nothing personal) 
The issue isn't one of Chinese monopolization of rare earth metal supplies. It's an issue of rare earth metal mining and export. Australia, India, and the US all have significant supplies, but simply are not utilizing them.
This is actually a good thing. Compare this to the oil market.
The United States has a significant reserve of oil in regions such as Alaska. Now, if these Alaskan reserves were in a desert in Texas or in a complete wasteland, the well would have been drilled long ago. Because, quite frankly, barring environmental issues, there really are no short term incentives against drilling for oil when one knows the oil is there... it's an instant moneymaker.
However, its presence in ANWAR creates an additional strain on politicians.
Here's the trick, though: I don't believe ANWAR is untouchable, except by its most ardent supporters. For example, assume OPEC did cut off oil shipments, and the US had not yet transitioned to an alternative energy source. Even if the US can purchase oil, the price per barrel would run through the roof. Or consider a WW2-esque military situation, in which the United States needed to supply a huge war machine (I'm talking total war mobilization, not that Iraq War-level mobilization). Under those circumstances, I don't believe anyone except the strongest environmental advocates would put the ANWAR environmental preservation over such a prevalent national security threat (remember, I'm talking most extreme circumstance).
So why is this important? Untapped supplies create mobilization reserves of scarce resources. Before World War 2, the United States and Japan were able to create a bitter economic war with one another, making the war itself inevitable. Before Pearl Harbor, the United States reprimanded Japanese expansion by embargoing exports of oil. At the time, with the US being their primary supplier, the Japanese were forced to take drastic measures to combat this problem, forcing them to speed up expansion in the hopes of either acquiring their own oil reserves or forcing the US to lift its own embargo.
Meanwhile, the US had its own resource shortage. Of particular note, Japan was able to conquer Malaya from the UK early in the war. That gave Japan control of 97% of the world's supply of rubber, which was necessary in pretty much every piece of mechanized military hardware. In recognition of this strategic difficulty, the US had to actually build up a strategic stockpile of rubber, similar to the strategic reserve of oil today. Meanwhile, the US would be funding development of synthetic rubbers, until the country could obtain independence from foreign imports of rubber (sound familiar?). In time, synthetic rubbers became more commonplace in the US, and although the rubbers at the time didn't match up to natural rubber, it became adequate enough for the military.
If you look, every country involved in the war inevitably had these resource issues of one type or another. For example, on the Eastern Front, Germany was within inches of knocking the Soviets out of the war by taking their #1 oil reserve in the Caucus region, which would have taken the Soviet tank and aerial forces out of commission (Hitler botched this up by ordering a redeployment of tanks and manpower for a simultaneous offensive in Stalingrad... and we all know what happened there). Economics wins wars. 
Anyway, those resources in ANWAR that we're talking about act in a very similar fashion. When oil prices are sitting at $20 a barrel, it's really difficult to make the case that a country needs to drill in the region. However, as the price steadily rises to $30, $40, and more, advocates can make a much better case in favor of drilling, to the point where it becomes prohibitively more expensive to maintain the environmental refuge. At some threshold (which could easily never actually manifest), the political opposition to drilling becomes so insurmountable that even its original opponents will be faced with too much opposition to resist a switch of opinions.
It's the same with rare earth metals. Currently, China is maxing out their reserve to supply to the world. I am 100% fine with that. Why? Because the US has its own strategic reserve of rare earth metals in case China ever decides to use that control to their political advantage. Meanwhile, China will be using up their reserves during the peacetime period. They'll make money, yes. However, for the time being, it's not a strategic resource. It's kind of the same as complaining that Japan monopolized the video game industry in the 1990's. Once it actually becomes a political issue, however, production can be kicked up in non-Chinese areas.
But this is definitely an interesting scenario nonetheless.