  We investigate the motion of electrically charged test particles in
spacetimes with closed timelike curves, a subset of the black hole or wormhole
Reissner-Nordstr\"om-NUT spacetimes without periodic identification of time. We
show that, while in the wormhole case there are closed worldlines inside a
potential well, the wordlines of initially distant charged observers moving
under the action of the Lorentz force can never close or self-intersect. This
means that for these observers causality is preserved, which is an instance of
our weak chronology protection criterion.
