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 < 500 Myr ago, but other work has hinted that older (> 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 +/- 0.17, i.e., D = 18.2 +/- 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 <V> and <I> 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 +/- 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 < 0.1) in the local universe.
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