  Variable stars have been identified for the first time in the very metal-poor
Blue Compact dwarf galaxy IZw18, using deep multi-band (F606W,
F814W)time-series photometry obtained with the Advanced Camera for Surveys
(ACS) on board the Hubble Space Telescope (HST). We detected 34 candidate
variable stars in the galaxy. We classify three of them as Classical Cepheids,
with periods of 8.71, 125.0 and 130.3 days, respectively, and other two as long
period variables with periodicities longer than a hundred days. These are the
lowest metallicity Classical Cepheids known so far, thus providing the
opportunity to explore and fit models of stellar pulsation fo Classical
Cepheids at previously inaccessible metallicities. The period distribution of
the confirmed Cepheids is markedly different from what is seen in other nearby
galaxies, which is likely related to the star bursting nature of IZw18. By
applying to the 8.71 days Cepheid theoretical Wesenheit (V,I) relations based
on new pulsation models of Classical Cepheids specifically computed for the
extremely low metallicity of this galaxy (Z=0.0004, Y=0.24), we estimate the
distance modulus of IZw18 to be mu_0= 31.4pm0.2 D=19.0^{+1.8}_{-1.7}Mpc) for
canonical models of Classical Cepheids, and of 31.2pm0.2 mag
(D=17.4^{+1.6}_{-1.6}Mpc) using over luminous models. The theoretical modeling
of the star's light curves provides mu_0=31.4pm0.1 mag, D=19.0^{+0.9}_{-0.9}
Mpc, in good agreement with the results from the theoretical Wesenheit
relations. These pulsation distances bracket the distance of 18.2pm1.5Mpc
inferred by Aloisi et al. (2007) using the galaxy's Red Giant Branch Tip.
