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 turn-offs, 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 Gyrs. 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, this implies that Cetus is a clear outlier in the morphology-Galactocentric distance relation that holds for the majority of Milky Way dwarf satellites. Our results also show that Cetus continued forming stars through z ~ 1, long after the Universe was reionized, and that there is no clear signature of the epoch of reionization in Cetus' SFH. We discuss briefly 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, COLE), and two stellar evolution libraries (BaSTI and Padova/Girardi), allowing for a detailed assessment of the modeling and observational uncertainties. Comment: 24 pages, 23 figures in emulateapj format. Submitted of ApJ. Several figures degraded. See http://www.iac.es/project/LCID/?p=publications for a version with full resolution figures