We present the first V, B-V color-magnitude diagram of the Leo IV dwarf spheroidal galaxy, a faint Milky Way satellite recently discovered by the Sloan Digital Sky Survey. We have obtained B,V time-series photometry reaching about half a magnitude below the Leo IV turnoff, which we detect at V= 24.7 mag, and have performed the first study of the variable star population. We have identified three RR Lyrae stars (all fundamental-mode pulsators, RRab) and one SX Phoenicis variable in the galaxy. In the period-amplitude diagram the Leo IV RR Lyrae stars are located close to the loci of Oosterhoff type I systems and the evolved fundamental-mode RR Lyrae stars in the Galactic globular cluster M3. However, their mean pulsation period, $<P{\rm ab}>$=0.655 days, would suggest an Oosterhoff type II classification for this galaxy. The RR Lyrae stars trace very well the galaxy's horizontal branch, setting its average magnitude at $<V_{\rm RR}>= 21.48 ± 0.03$ mag (standard deviation of the mean). This leads to a distance modulus of $μ_{0}=20.94 ± 0.07$ mag, corresponding to a distance of $154 ± 5$ kpc, by adopting for the Leo IV dSph a reddening $E(B-V) = 0.04 ± 0.01$ mag and a metallicity of [Fe/H] = -2.31 $±$ 0.10. Comment: 14 pages, 4 figures, accepted for publication on The Astrophysical Journal Letters