The dynamics on a three-dimensional energy shell of the planar circular restricted three-body problem are analyzed. Local chaos is seen to occur in this Hamiltonian system in the regions between the KAM tori, and is caused by the intersection of stable and unstable manifolds of periodic orbits in what Poincare called the "homoclinic trellis." We investigate the trellis, or tangle, by means of lobe dynamics, in order to describe and quantify barriers in the phase space and transport "alleyways." Furthermore, numerical experiments suggest that there are energy intervals in which the motion approaches ergodicity, i.e., the time average of any smooth observable along almost any trajectory can be replaced by the microcanonical average of that observable. These calculations suggest that further development of a statistical theory within the restricted three-body model will be a fruitful approach to astrodynamical problems.