The kinetic motion of the stars of a galaxy is considered within the framework of a relativistic scalar theory of gravitation. This model, even though unphysical, may represent a good laboratory to study in a rigorous, mathematical way those problems, such as the influence of the gravitational radiation on the dynamics, which are still beyond our present understanding of the physical model represented by the Einstein–Vlasov system. The present paper is devoted to deriving the equations of the model and to proving the existence of spherically symmetric equilibria with finite radius.