The stability of planetary motion in the binary system α Cen A-B is studied. Lyapunov spectra of the motion of the system with a single massive planet are computed on a fine grid of the initial data, and, by means of statistical analysis of the obtained data arrays, chaotic domains are identified in the pericentric distance - eccentricity initial data space for the planetary orbit. Association with the initial data domains for the orbits exhibiting close encounters with central stars and for the orbits exhibiting long-term escape is investigated.