A more detailed assessment:

http://www.fas.org/sgp/crs/natsec/R41347.pdf

It is important to note that "rare earths" are not particularly rare, and that China dominates the market not because it has unique reserves, but because it sold the product cheap for a long time, rendering other suppliers unprofitable. While the time required to restart old mines and bring new ones onstream is a real concern, some of the more panicked comments about Chinese control of rare earths are more than a bit exaggerated.