A pair of eyeglass holders is designed to engage over the lower rims of respective opposite side portions of a hat, visor, or other headwear. Each eyeglass holder has a spring clip for gripping the respective hat side portion and a retainer or gripper secured to an outer leg of the spring clip. The grippers are designed to engage and releasably retain the respective arms of a pair of glasses with the glasses in an inverted orientation. Each gripper is secured to the outer leg of the associated clip to extend upwardly from a location closer to the lower end than the upper end of the clip so as to hold the respective arm of the glasses at a location relatively close to the lower rim of the hat.