Why, yes it does. Quite a bit as a matter of fact. The following is from the Mainichi.

The Japanese government shoulders part of the cost for stationing U.S. forces in Japan, known in Japanese as "Omoiyari yosan" (an appreciation payment), or as host nation support (HNS).
In the fiscal 2009 budget, the "consideration" stood at a cool 192.8 billion yen.

:O

A few months ago someone who works for CFAY in an office that monitors the utility bills, told me that the Japanese Government pays about 75% of the entire electric bill on the American bases here in Japan. The current party in power is not very pro-American, so sooner or later they will come down on us like a ton of bricks about blatant waste of electricity. So, think about that next time you leave your lights on while you know IF YOU were paying for it, you would turn them off!