Supersymmetry and R_b in the light of LEP 1.5

We re-examine the possible magnitude of the supersymmetric contribution to $R_b\equiv\Gamma(Z^0\to\bar b b)/\Gamma(Z^0\to{\rm all})$ in the light of the constraints imposed by the absence of light charginos at LEP~1.5, implementing also other available phenomenological constraints. We find the supersymmetric contribution to be $R^{\rm susy}_b < 0.0017$, and discuss the extent to which this upper bound could be strengthened by future constraints on the chargino and top-squark masses. Such values of $R^{\rm susy}_b$ tend to disfavor a supersymmetry explanation of the apparent $R_b$ discrepancy.