Observations show a prevalence of high redshift galaxies with large stellar masses and predominantly passive stellar populations. A variety of processes have been suggested that could reduce the star formation in such galaxies to observed levels, including quasar mode feedback, virial shock heating, or galactic winds driven by stellar feedback. However, the main quenching mechanisms have yet to be identified. Here we study the origin of star formation quenching using Argo, a cosmological, hydrodynamical zoom-in simulation that follows the evolution of a massive galaxy at z 2. This simulation adopts the same sub-grid recipes of the Eris simulations, which have been shown to form realistic disk galaxies, and, in one version, adopts also a mass and spatial resolution identical to Eris. The resulting galaxy has properties consistent with those of observed, massive (M * ∼ 10 11 M ) galaxies at z ∼ 2 and with abundance matching predictions. Our models do not include AGN feedback indicating that supermassive black holes likely play a subordinate role in determining masses and sizes of massive galaxies at high z. The specific star formation rate (sSFR) of the simulated galaxy matches the observed M * -sSFR relation at early times. This period of smooth stellar mass growth comes to a sudden halt at z = 3.5 when the sSFR drops by almost an order of magnitude within a few hundred Myr. The suppression is initiated by a leveling off and a subsequent reduction of the cool gas accretion rate onto the galaxy, and not by feedback processes. This "cosmological starvation" occurs as the parent dark matter halo switches from a fast collapsing mode to a slow accretion mode. Additional mechanisms, such as perhaps radio mode feedback from an AGN, are needed to quench any residual star formation of the galaxy and to maintain a low sSFR until the present time.