The synchronized modes of two-coupled Oregonator models are investigated. The numerical results indicate that the combination of the time delay and asymmetry in the coupling between the independent oscillators generates the chaotic oscillations. This study also reveals the two types of routes to chaos of anti-phase mode → chaos → anti-phase mode and in-phase mode → chaos → anti-phase mode. Furthermore, we propose an equation for the one-dimensional map of the chaos observed in the two-coupled Oregonators.