Place tuna steaks and olive oil in a large resealable plastic bag. Seal, and refrigerate for 1 hour.
Preheat the grill for medium heat. When coals are very hot, scatter a handful of hickory or mesquite wood chips over them for flavor.
Lightly oil grill grate. Season tuna with salt and pepper, and cook on the preheated grill approximately 6 minutes, turning once. Transfer to a serving platter, and drizzle with freshly squeezed lime juice. Serve immediately.