When all I had to cook out on was an hibachi grill, I often put chicken breasts in a pan, added whatever seasonings and marinade I wanted, and put them in a slow oven (F 300 degrees)for about 30-45 minutes.
Then I'd take them out, pour off the marinade and then cook the chicken on the hibachi, adding any kind of sauce I might want to finish it with. I considered this an essential procedure since the coals in the hibachi did not last long enough to cook raw chicken sufficiently through. (It was a small hibachi!).