Using hybrid functional calculation, we identify the key intrinsic defects in Cu2ZnSnS4 (CZTS), an important earth-abundant solar-cell material. The Sn-on-Zn antisite and the defect complex having three Cu atoms occupying a Sn vacancy are found to be the main deep electron traps. This result explains the optimal growth condition for CZTS, which is Cu poor and Zn rich, as found in several recent experiments. We show that, under the growth condition that minimizes the deep traps, Cu vacancy could contribute the majority of hole carriers, while the Cu-on-Zn antisite will become the dominant acceptor if the growth condition favors its formation.