A preform for forming a hollow blow molded plastic container is provided with a closed base, a multilayer body-forming portion extending from the base, and an open neck portion that extends from the body portion. The body portion includes a co-extruded inner liner that includes (a) an innermost polymer layer, (b) at least one oxygen-scavenging layer, and (c) at least one high-oxygen barrier layer for retarding the migration of gases and moisture therethrough. An outermost layer is molded over the inner liner to form a preform. The liner and preform are formed so that the wall thickness of the individual layers can easily be varied along their lengths, however, at any given point along the length of the co-extruded liner (a) the wall thickness of the innermost polymer layer is less than 0.50 of the wall thickness of the inner liner and (b) the wall thickness of the inner liner is less than 0.25 of the total wall thickness of the preform body portion. Moreover, by the nature of the process, the innermost layer and the outer molded layer of the liner and the preform can be comprised of different polymer materials.