We present the results of a search for short-period variable stars in Leo A. We have found 92 candidate variables, including eight candidate RR Lyrae stars. From the RR Lyraes, we measure a distance modulus of (m-M)_0 = 24.51 +/- 0.12, or 0.80 +/- 0.04 Mpc. This discovery of RR Lyraes confirms, for the first time, the presence of an ancient (> ~11 Gyr) population in Leo A accounting for at least 0.1% of the galaxys V luminosity. We have also discovered a halo of old (> ~2 Gyr) stars surrounding Leo A, with a scale length roughly 50% larger than that of the dominant young population. We also report the discovery of a large population of Cepheids in Leo A. The median absolute magnitude of our Cepheid sample is M_V = -1.1, fainter than 96% of SMC and 99% of LMC Cepheids. Their periods are also unusual, with three Cepheids that are deduced to be pulsating in the fundamental mode having periods of under 1 day. Upon examination, these characteristics of the Leo A Cepheid population appear to be a natural extension of the classical Cepheid period-luminosity relations to low metallicity, rather than being indicative of a large population of ``anomalous Cepheids. We demonstrate that the periods and luminosities are consistent with the expected values of low-metallicity blue helium-burning stars (BHeBs), which populate the instability strip at lower luminosities than do higher-metallicity BHeBs.
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