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 \pm 0.12 , or 0.80 \pm 0.04 Mpc . This discovery of RR Lyraes confirms , for the first time , the presence of an ancient ( > \sim 11 Gyr ) population in Leo A accounting for at least 0.1 % of the galaxy ’ s V luminosity . We have also discovered a halo of old ( > \sim 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 .