We experimentally and numerically show that chirality can play a major role in the nonlinear optical response of soft birefringent materials, by studying the nonlinear propagation of laser beams in frustrated cholesteric liquid crystal samples. Such beams exhibit a periodic nonlinear response associated with a bouncing pattern for the optical fields, as well as a self-focusing effect enhanced by the chirality of the birefringent material. Our results open new possible designs of nonlinear optical devices with low power consumption and tunable interactions with localized topological solitons.