A potato cultivar designated J3 is disclosed. The invention relates to tubers of potato cultivar J3, to seeds of potato cultivar J3, to plants and plant parts of potato cultivar J3, to food products produced from potato cultivar J3, and to methods for producing a potato plant by crossing potato cultivar J3 with itself or with another potato variety. The invention also relates to methods for producing a transgenic potato plant and to the transgenic potato plants and parts produced by those methods. This invention also relates to potato plants and plant parts derived from potato cultivar J3, to methods for producing other potato plants or plant parts derived from potato cultivar J3 and to the potato plants and their parts derived from use of those methods. The invention further relates to hybrid potato tubers, seeds, plants and plant parts produced by crossing potato cultivar J3 with another potato cultivar.