Headwear in which a storage area or pocket is formed in one side of the hat portion where an accessory is stored in the pocket when not in use. The free end of the accessory can be removed from the pocket by the wearer and pulled across the wearer's face after which the free end of the accessory is detachably secured to an opposite side of the hat portion so that the accessory remains positioned over the wearer's face. After use, the free end of the accessory is detached from the hat portion and returned for storage in the pocket. The invention is described in an embodiment for use in a ski hat in which the accessory is a goggle. Also described is the provision of a non-permeable layer in the hat portion that prevents moisture from reaching the goggle to prevent it from fogging up during its use.