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 on board the Hubble Space Telescope. 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 100 days. These are the lowest metallicity Classical Cepheids known so far, thus providing the opportunity to explore and fit models of stellar pulsation for 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. The long period Cepheids we have detected in IZw18 seem to indicate that massive stars at the metallicity of IZw18 (Z = 0.0004) may cross the instability strip long enough to be observed. 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 μ0 = 31.4 ± 0.3 (D = 19.0+2.8 –2.5 Mpc) for canonical models of Classical Cepheids, and of 31.2 ± 0.3 mag (D = 17.4+2.6 –2.2 Mpc) using over luminous models. The theoretical modeling of the star's light curves provides μ0 = 31.4± 0.2 mag, D = 19.0+1.8 –1.7 Mpc, in good agreement with the results from the theoretical Wesenheit relations. These pulsation distances bracket the distance of 18.2 ±1.5 Mpc inferred by Aloisi et al. using the galaxy's red giant branch tip.