  Due to the observation of Bose-Einstein condensation in dilute atomic
$^{87}$Rb and $^{23}$Na vapors last year, there is currently a great interest
in the properties of a degenerate Bose gas. One aspect that is not yet
understood is the effect of the interatomic interactions on the critical
temperature of the phase transition. We present here a renormalization group
study of the weakly-interacting Bose gas and predict the critical temperature
at which Bose-Einstein condensation occurs as a function of the (positive)
scattering length $a$ of the interatomic potential.
