At zero temperature a system of integer spin particles all occupy the same quantum state. In the absence of gravity this is a zero momentum state which therefore has zero pressure. If the effect of self-gravity is included however, the wave function can satisfy the Schrodinger equation in the self-consistent gravitational field of the corresponding probability density distribution. Such a configuration is known as a boson star. The question arises as to what the maximum mass (if any) of such a star might be.