Propagation in a Kerr medium of a system of equal-frequency light waves has been studied, each of the waves being involved in two four-wave mixing processes. Competition of these processes is shown to result in non-integrability and chaos. A stochastic regime of evolution sets in if the input values of the wave amplitudes differ strongly enough from the ones corresponding to the integrable limit connected with the system symmetry. Another condition for the chaos—strong energy exchange between the waves—is realized when the medium and radiation parameter values have the same order of magnitude as those required to obtain enhanced phase-conjugate reflection due to degenerate four-wave mixing. Various manifestations of stochastic instability of the system of light waves under experimental conditions are also discussed.