The planet recently discovered(1) orbiting the star 16 Cyg B has the largest eccentricity (e = 0.67) of any known planet, Planets that form in circumstellar disks are expected to have nearly circular orbits, although gravitational interactions in a system of two or more planets could generate high-eccentricity orbits(2,3). Here we suggest that the eccentric orbit of 16 Cyg Bb arises from gravitational interactions with the distant companion star, 16 Cyg A, Assuming that 16 Cyg Bb formed in a nearly circular orbit, with the orbital plane inclined between 45 degrees and 135 degrees to the orbital plane of 16 Cyg A, and that there are no other planets with a mass similar to that of Jupiter within 30 astronomical units (hv, the average distance between the Earth and the Sun), then 16 Cyg Bb will oscillate between low-eccentricity and high-eccentricity orbits, The transitions between these orbits should occur every 10(7)-10(9) years, with the planet spending up to 35 per cent of its lifetime with an eccentricity e > 0.6, These results imply that planetary orbits in binary stellar systems commonly experience periods of high eccentricity and dynamical chaos, and that such planets may occasionally collide with the primary star.