A tissue welding apparatus is adapted to fuse a first piece of tissue to a second piece of tissue which are disposed in a surface proximate relationship. An elongate shaft carries a first jaw, and a second opposing jaw moveable relative to the first jaw. At least one penetrating member is carried by the first jaw and moveable relative to the second jaw to create a channel through the first piece of material and the second piece of material. A source of heat is coupled to the penetrating member for denaturing the tissue defining the channel. This denatured tissue forms a column binding the first piece of tissue to the second piece of tissue. A chemical agent can be carried to the tissue with the penetrating member.