HDPE nanocomposite is made by mixing HDPE with organoclay. Such HDPE nanocomposite contains concentrations of organoclay less than 4 weight percent. Unexpectedly, using less organoclay than that conventionally recommended, results in superior oxygen and water vapor transmission rates for HDPE compounds. The HDPE nanocomposite is useful for packaging films and containers for food or other perishables.