We report the discovery of variable stars in the dwarf elliptical galaxy M32 using a series of images obtained with the Wide Field Planetary Camera 2 on the Hubble Space Telescope. The colors, luminosities, and approximate periods of the majority of these stars indicate that they are RR Lyrae stars. Comparisons with the number of such stars identified in a nearby control field reveals that the majority of these variable stars are M32 members and not contaminants from the bulge, halo, or thick disk of the Andromeda Galaxy, M31. This discovery of RR Lyrae stars in M32 provides strong evidence of the presence of an "ancient" stellar population in this enigmatic galaxy. Although it is not possible with our data to provide a precise age estimate of the population from which the M32 RR Lyrae stars arise, we argue that these stars almost certainly represent a component that is older than 10 Gyr. Due to the sensitivity of the horizontal branch—and therefore the population of the instability strip—to age and metallicity among other parameters, we roughly estimate that this old and metal-poor component represents at least 2.3% of the total stellar population of M32.