We have discovered the first example of a star pulsating intrinsically with both {gamma} Doradus and {delta} Scuti frequencies. HD 8801 is an Am metallic-line star that appears to be single. Since the vast majority of Am stars are members of binary systems with periods less than 1000 days and also do not pulsate, HD 8801 possesses a very unusual, if not unique, combination of physical properties. Our photometry, acquired with an automatic telescope at Fairborn Observatory, resolves six independent pulsation periods between 0.048 and 0.404 days. The two longest periods lie within the range of {gamma} Dor variables, while the four shorter periods are within the range of {delta} Sct stars.