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