One of the common features of unconventional superconducting systems such as the heavy-fermion, high transition-temperature cuprate and iron-pnictide superconductors is that the superconductivity emerges in the vicinity of long-range antiferromagnetically ordered state. In addition to doping charge carriers, the application of external pressure is an effective and clean approach to induce unconventional superconductivity near a magnetic quantum critical point. Here we report on the discovery of superconductivity on the verge of antiferromagnetic order in CrAs via the application of external pressure. Bulk superconductivity with Tc≈2 K emerges at the critical pressure Pc≈8 kbar, where the first-order antiferromagnetic transition at T(N)≈265 K under ambient pressure is completely suppressed. The close proximity of superconductivity to an antiferromagnetic order suggests an unconventional pairing mechanism for CrAs. The present finding opens a new avenue for searching novel superconductors in the Cr and other transition metal-based systems.