  We find new spherically symmetric charged boson star solutions of a complex
scalar field coupled non-minimally to gravity by a "John-type" term of
Horndeski theory, that is a coupling between the kinetic scalar term and
Einstein tensor. We study the parameter space of the solutions and find two
distinct families according to their position in parameter space. More
widespread is the family of solutions (which we call branch 1) existing for a
finite interval of the central value of the scalar field starting from zero and
ending at some finite maximal value. This branch contains as a special case the
charged boson stars of the minimally coupled theory. In some regions of
parameter space we find a new second branch ("branch 2") of solutions which are
more massive and more stable than those of branch 1. This second branch exists
also in a finite interval of the central value of the scalar field, but its end
points (either both or in some cases only one) are extremal Reissner-Nordstrom
black hole solutions.
