  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 $<V_{\rm RR}>= 21.48 \pm 0.03$ mag (standard deviation of the
mean). This leads to a distance modulus of $\mu_{0}=20.94 \pm 0.07$ mag,
corresponding to a distance of $154 \pm 5$ kpc, by adopting for the Leo IV dSph
a reddening $E(B-V) = 0.04 \pm 0.01$ mag and a metallicity of [Fe/H] = -2.31
$\pm$ 0.10.
