Place tuna steaks and olive oil in a large resealable plastic bag. Seal and refrigerate for 1 hour.
Preheat barbecue for medium heat. When coals are very hot, scatter a handful of hickory chips over them for flavour.
Lightly oil the cooking grate. Season tuna with salt and pepper and grill on the preheated barbecue approximately 6 minutes, turning once. Transfer to a serving plate and drizzle with freshly squeezed lime juice. Serve immediately.
Alternative cooking methods
The tuna steaks can also be cooked under the grill.