A brief analysis of the dynamics of a Friedmann-Robertson-Walker universe with a conformally coupled, real, self-interacting, massive scalar field, based on the Painleve theory of differential equations, is presented. Our results complete earlier works done within the framework of Dynamical System Theory. We conclude that, in general, the system will not be integrable and that the chaos that has been found in a previous work, arises from the presence of movable logarithmic branch points in the solution in the complex plane of time.Facultad de Ciencias Astronómicas y Geofísicas