  `Gravitational memory' refers to the possibility that, in cosmologies with a
time-varying gravitational `constant', objects such as black holes may retain a
memory of conditions at the time of their birth. We consider this phenomenon in
a different physical scenario, where the objects under consideration are boson
stars. We construct boson star solutions in scalar-tensor gravity theories, and
consider their dependence on the asymptotic value of the gravitational
strength. We then discuss several possible physical interpretations, including
the concept of pure gravitational stellar evolution.
