  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 galaxy's 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.
