Achieving the regime of single-photon nonlinearities in photonic devices by just exploiting the intrinsic high-order susceptibilities of conventional materials would open the door to practical semiconductor-based quantum photonic technologies. Here we show that this regime can be achieved in a triply resonant integrated photonic device made of two coupled ring resonators, in a material platform displaying an intrinsic third-order nonlinearity. By strongly driving one of the three resonances of the system, a weak coherent probe at one of the others results in a strongly suppressed two-photon probability at the output, evidenced by an antibunched second-order correlation function at zero-time delay under continuous wave driving.