Combine first five ingredients in a small bowl; stir well, and set aside.
Sprinkle salt and pepper over the tuna steaks.
Using 2 tablespoons of apple chips, smoke tuna steaks for twenty minutes over medium heat. This should leave the steaks medium-rare. Do not overcook.
Serve with the steaks with the herbed mayonnaise sauce and a tossed salad on the side and you have a tasty, healthy dinner.