We present new V and I -band HST/ACS photometry of I Zw 18 , the most metal-poor blue compact dwarf ( BCD ) galaxy in the nearby universe . It has been argued in the past that I Zw 18 is a very young system that started forming stars only \lesssim 500 Myr ago , but other work has hinted that older ( \gtrsim 1 Gyr ) red giant branch ( RGB ) stars may also exist . Our new data , once combined with archival HST/ACS data , provide a deep and uncontaminated optical color-magnitude diagram ( CMD ) that now strongly indicates an RGB . The RGB tip ( TRGB ) magnitude yields a distance modulus ( m - M ) _ { 0 } = 31.30 \pm 0.17 , i.e. , D = 18.2 \pm 1.5 Mpc . The time-series nature of our observations allows us to also detect and characterize for the first time three classical Cepheids in I Zw 18 . The time-averaged Cepheid \langle V \rangle and \langle I \rangle magnitudes are compared to the VI reddening-free Wesenheit relation predicted from new non-linear pulsation models specifically calculated at the metallicity of I Zw 18 . For the one bona-fide classical Cepheid with a period of 8.63 days this implies a distance modulus ( m - M ) _ { 0 } = 31.42 \pm 0.26 . The other two Cepheids have unusually long periods ( 125.0 and 129.8 d ) but are consistent with this distance . The coherent picture that emerges is that I Zw 18 is older and farther away than previously believed . This rules out the possibility that I Zw 18 is a truly primordial galaxy formed recently ( z \lesssim 0.1 ) in the local universe .