We use deep HST/ACS observations to calculate the star formation history (SFH) of the Cetus dwarf spheroidal (dSph) galaxy. Our photometry reaches below the oldest main-sequence turnoffs, which allows us to estimate the age and duration of the main episode of star formation in Cetus. This is well approximated by a single episode that peaked roughly 12 ± 0.5 Gyr ago and lasted no longer than about 1.9 ± 0.5 Gyr (FWHM). Our solution also suggests that essentially no stars formed in Cetus during the past 8 Gyr. This makes Cetus' SFH comparable to that of the oldest Milky Way dSphs. Given the current isolation of Cetus in the outer fringes of the Local Group, the dominant old population implies that Cetus is a clear outlier in the morphology-Galactocentric distance relation that holds for the majority of the Milky Way dwarf satellites. Our results also show that Cetus continued forming stars until zsime 1, long after the universe was reionized, and that there is no clear signature of the epoch of reionization in Cetus' SFH. We briefly discuss the implications of these results for dwarf galaxy evolution models. Finally, we present a comprehensive account of the data reduction and analysis strategy adopted for all galaxies targeted by the LCID (Local Cosmology from Isolated Dwarfs) project. We employ two different photometry codes (DAOPHOT/ALLFRAME and DOLPHOT), three different SFH reconstruction codes (IAC-pop/MinnIAC, MATCH, and COLE), and two stellar evolution libraries (BaSTI and Padova/Girardi), allowing for a detailed assessment of the modeling and observational uncertainties. Based on observations made with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. These observations are associated with program 10505.