A method of making a plastic container that has a tethered closure using an extrusion blow molding process includes steps of extruding a parison, capturing the parison within a mold and inflating the parison against the mold to form a container blank having a container portion, a closure portion and a tether portion for connecting the container portion to the closure portion. The tether portion, which is preferably elongated and string like, may be formed out of flash material that is created during the molding process. The resulting container is relatively inexpensive to manufacture and facilitates the plastic recycling process.