We determine the critical temperature of a 3D homogeneous system of ha
rd-sphere bosons by pathintegral Monte Carlo simulations and finite-si
ze scaling. In the low density limit, we find that the critical temper
ature is increased by the repulsive interactions, as Delta T-C/T-0 sim
ilar to (na(3))(gamma), where gamma = 0.34 +/- 0.03. At high densities
the result for liquid helium, namely, a lower critical temperature th
an in the noninteracting case, is recovered. We give a microscopic exp
lanation for the observed behavior. [S0031-9007(97)04438-4].