An envelope has an envelope body formed by opposing panels that define an interior and an opening. A closure is joined to and extends up from the top margin of one panel. The envelope is configured such that the interior surface of the closure is sealable to the other panel to permanently close the envelope opening. The closure includes a closure panel and a tear band coextruded with the closure panel. The tear band is composed of a polymeric material having lower tear strength than the material of the closure panel. The tear band defines a zone of weakness extending along the width of the closure for opening the closure by tearing along the zone of weakness after it is permanently closed.