This talk deals with a semilinear elliptic system, called the O(3) Maxwell-Chern-Simons equations, on a two-dimensional flat torus. This system arises from the O(3) sigma gauge field model. The system has three important parameters au in [0,1], and κ, q > 0. For au ∈ [0, 1), there are several known results on the existence of solutions. However, no results have been reported for the case of au = 1. In this talk, we focus on the case of au = 1 and show that the system possesses a solution pair for a sufficiently small κ>0 and a very large q>0.