In an attractive Coulomb electric field and a uniform magnetic field B, some particle orbits originating at infinite distance undergo many reflections, repeated approaching the Coulomb centre. The chaotic nature of these orbits is discussed and illustrated by numerical calculations. The divergence of neighboring trajectories is shown to occur mostly in discrete jumps when they pass near the Coulomb centre. The appearance of chaotic behaviour in this simplified situation suggests that it will also occur when space-charge effects significantly perturb the potential distribution around a current-collecting electrode in a space magnetoplasma. ¿American Geophysical Union 1991