This paper investigates the long-term orbital stability of small bodie
s 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 semimajor axes less than roughly three tim
es the binary's semimajor axis ab are unstable. Inside the binary, par
ticles are unstable if further than 4 AU from either star, with stabil
ity closer in a strong function of inclination on the time scale of th
ese integrations: orbits inclined near 90 degrees are unstable in as c
lose as 0.23 AU from either star. We also present charts of the predic
ted stable regions as projected against the plane of the sky to aid di
rect imaging searches. (C) 1997 American Astronomical Society.