We present results from new deep HST/ACS photometry of I Zw 18, the most metal-poor blue compact dwarf galaxy in the nearby universe. It has been previously argued that this is a very young system that started forming stars only ≲500 Gyr ago, but other work has hinted that older (≳1 Gyr) red giant branch (RGB) stars may exist in this galaxy. Our deeper data indeed reveal evidence for an RGB. Underlying old (≳1 Gyr) populations are therefore present in even the most metal-poor systems, implying that star formation started at z ≳ 0.1. The RGB tip (TRGB) magnitude and the properties of Cepheid variables identified from our program indicate that I Zw 18 is farther away (D = 19.0 ± 1.8 Mpc) than previously believed.