We have discovered the first example of a star pulsating intrinsically with both γ Doradus and δ Scuti frequencies. The star, 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 γ Dor variables, while the four shorter periods are within the range of δ Sct stars. Eleven radial velocities, obtained over an 11 month period, have a mean of 0.8 ± 0.3 km s^-1, providing no evidence for a spectroscopic companion. The star is on the main sequence and lies within both the γ Dor and δ Sct instability strips. Pulsation constants computed for the six periods agree with pulsation constants computed for other γ Dor and δ Sct variables. HD 8801 is also the first confirmed case of a metallic-line star pulsating with γ Dor frequencies. Its projected rotational velocity of 55 km s^-1 is typical for Am stars, which, as a group, rotate more slowly than normal A stars. HD 8801's slow rotation compared to normal A stars does not appear to arise from either a binary companion or evolutionary expansion and thus remains a puzzle. The coexistence of metallicism and pulsation in several main-sequence stars near the red edge of the δ Sct strip contradicts recent models that predict pulsations only in more evolved stars.