We present a cosmological hydrodynamic simulation of the formation of dwarf galaxies at redshifts z \gtrsim 2.5 using a physically-motivated model for H _ { 2 } -regulated star formation . Our simulation , performed using the Enzo code and reaching a peak resolution of 109 proper parsecs at z = 2.5 , extends the results of to significantly lower redshifts . We show that a star formation prescription regulated by the local H _ { 2 } abundance leads to the suppression of star formation in dwarf galaxy halos with M _ { h } \lesssim 10 ^ { 10 } M _ { \odot } and to a large population of gas-rich “ dark galaxies ” at z = 2.5 with low star formation efficiencies and gas depletion timescales > 20 Gyr . The fraction of dark galaxies is 60 % at M _ { h } \simeq 10 ^ { 10 } M _ { \odot } and increases rapidly with decreasing halo mass . Dark galaxies form late and their gaseous disks never reach the surface densities , \gtrsim 5700 M _ { \odot } { pc } ^ { -2 } ( Z / 10 ^ { -3 } Z _ { \odot } ) ^ { -0.88 } , that are required to build a substantial molecular fraction . Despite this large population of dark galaxies , we show that our H _ { 2 } -regulated simulation is consistent with both the observed luminosity function of galaxies and the cosmological mass density of neutral gas at z \gtrsim 2.5 . Moreover , our results provide a theoretical explanation for the recent detection in fluorescent Ly \alpha emission of gaseous systems at high redshift with little or no associated star formation . We further propose that H _ { 2 } -regulation may offer a fresh solution to a number of outstanding “ dwarf galaxy problems ” in \Lambda CDM . In particular , H _ { 2 } -regulation leads galaxy formation to become effectively stochastic on mass scales of M _ { h } \sim 10 ^ { 10 } M _ { \odot } , and thus these massive dwarfs are not “ too big to fail ” .