Chiral superconductivity emerges in three-band superconductors when interband interactions are much smaller than intraband interactions and either one or three interband interactions are positive. The chiral ground states are demonstrated using the phenomenological Ginzburg–Landau free energy modeling of three-component superconductivity based on a three-band superconductor. The origin of chiral superconductivity in three-band superconductors is different from that of the conventional time reversal symmetry breaking states such as triplet superconductivity and d + i s wave.