Combine all the marinade ingredients in a bowl large enough to hold the tuna. Place the tuna steaks in the marinade and refrigerate for 3 hours, turning every hour.
Drain the tuna thirty minutes before cooking and bring to room temperature.
Preheat a grill, grill pan or outdoor barbecue to very hot.
Brush the tuna with olive oil. Grill the steaks for 1 to 2 minutes on each of their six sides. The outside of the tuna should be nicely charred, and the center should be barely warm and quite rare. Cooked this way, the tuna will remain moist and flavorful.