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 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 \mu _ { 0 } = 31.4 \pm 0.3 ( D=19.0 ^ { +2.8 } _ { -2.5 } Mpc ) for canonical models of Classical Cepheids , and of 31.2 \pm 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 \mu _ { 0 } = 31.4 \pm 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 \pm 1.5 Mpc inferred by using the galaxy ’ s Red Giant Branch Tip .