This paper investigates the long-term orbital stability of small bodies near the central binary of the Alpha Centauri system. Test particles on circular orbits are integrated in the field of this binary for 32 000 binary periods or approximately 2.5 Myr. In the region exterior to the binary, particles with semi-major axes less than roughly three times the binary's semi-major axis a_b are unstable. Inside the binary, particles are unstable if further than 4 AU from either star, with stability closer in a strong function of inclination on the time scale of these integrations: orbits inclined near 90degree are unstable in as close as 0.23 AU from either star. We also present charts of the predicted stable regions as projected against the plane of the sky to aid direct imaging searches.