We consider the planar circular restricted three body problem, modeling the motion of a massless asteroid in the plane undergoing gravitational attraction toward two bodies, each with a circular orbit around their center of mass. For small mass ratios, this is approximated by the Kepler problem as long as the asteroid remains far from the smaller body. The existence of hyperbolic sets containing orbits in which the asteroid undergoes repeated close interactions with the smaller body was proven independently by Bolotin and MacKay and by Font, Nunes, and SimÃ³. My conjecture is that there are elliptic periodic orbits with repeated close interactions, where the asteroid remains close to a Kepler ellipse intersecting the orbit of the smaller body.