We propose a theoretical scheme to achieve nonreciprocal universal photon blockade (PB) in a chiral coupled-cavity system. This approach utilizes the synergistic effect of chiral asymmetry and two-photon quantum interference: by embedding a two-level atom described by the two-photon Jaynes-Cummings (JC) model within one of the optical cavities, specific excitation pathways can be induced by tuning the phase and intensity of the external driving field. We demonstrate that under forward driving, the external driving field and the internal two-photon JC model coupling produce destructive quantum interference, thereby effectively suppressing two-photon excitation and achieving a high-quality single-photon PB. However, under backward driving, due to the chiral asymmetry of the system, the phase-matching condition for destructive interference is completely broken, and the PB phenomenon subsequently disappears. Our findings provide a promising approach for designing high-performance nonreciprocal single-photon sources and quantum isolation devices.