If you love turkey but prefer to eat just the white meat, then grilling a turkey breast is a great way to get all of the flavor without the mess of preparing a full turkey dinner in the oven. Grilling the turkey on the gas grill seals in the juices and gives the turkey breast a crisp, browned skin that is difficult to achieve in the oven without overcooking the breast itself. If you like turkey sandwiches, prepare two breasts instead of one so that you have leftovers.
Combine 1 cup olive oil, 3 sprigs fresh rosemary, 1 tsp. minced garlic, 1 tbsp. kosher salt and 1 tsp. ground pepper in a 2.5 gallon plastic bag. Add a 5 lb. bone-in turkey breast and seal the plastic bag, gently shaking the marinade around the meat. Marinate the turkey in the refrigerator for four hours, and set it out on the kitchen counter for one hour before cooking to bring the meat to room temperature.
Preheat your gas grill to high. Put the turkey breast on the grill with the bone facing down, and lower the grill temperature setting to medium. Insert your remote cooking thermometer probe into the thickest part of the turkey breast and turn the thermometer on at the base. Close the grill hood.
After 30 minutes, when the cooking thermometer registers approximately 100 degrees, add a handful of fruit wood chips to your smoking box and put it in the back section of the grill.
Pour one cup of chicken stock into a disposable aluminum pan, and place the turkey breast in the pan with the bone still facing down. Keep the cooking thermometer probe in, and cover the pan with aluminum foil. Turn the grill heat setting down to low in the back, turn the front burner off entirely, and move the aluminum pan to the front of the grill. Close the grill and allow the turkey breast to finish cooking for approximately 30 more minutes, until the thermometer reads 163 degrees.
Turn off the grill, transfer the turkey breast to a platter and wait five minutes to allow the internal temperature of the turkey to finish rising to 165 degrees. Remove the thermometer probe and serve.