Oil leases from whom?

We hear a lot nowadays about China, Vietnam and other countries leasing oil drilling rights off the coasts of the United States. Who are they leasing this maritime territory to drill oil from?

U.S. territorial waters extend three miles from the coast line. I always thought that everything beyond three miles was a sort of no-man's land (no-man's water, if you will), having jurisdiction by no one.

Why do other countries need a "lease" to drill oil off the American coasts? A lease from whom?