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Soak wood chips in enough water to cover for about 30 minutes. Drain. Place about 1 cup wood chips in center of each of 3 sheets of aluminum foil. Fold tightly to make 3 packets. Poke several holes with fork on both sides of packets to allow smoke to escape. Set aside.
Prepare grill for indirect medium heat (350°F to 375°F). Preheat grill by turning all burners to medium.
Rub turkey lightly with oil. Rub cavity with 1 tablespoon of the Seasoning. Sprinkle remaining Seasoning under skin and over surface of turkey. Place turkey in large disposable aluminum pan.
Turn off burner(s) on one side of grill. Place 1 foil packet directly on grill rack over lit burner. Reserve remaining packets.
Place turkey in pan on unlit side of grill. Close lid. Grill about 3 hours or until cooked through (internal temperature of breast reaches 165°F and thigh is 175°F). Refresh grill with a fresh packet of wood chips every hour for maximum smoke flavor. Remove pan from grill. Let stand 20 minutes. Transfer turkey to platter or carving board to slice.