We analyze the one loop corrections to hadronic Z decays in an R-parity violating extension to the minimal supersymmetric standard model. Performing a global fit to all the hadronic observables at the Z peak, we obtain stringent constraints on the R-violating coupling constants lambda' and lambda". The presence of these couplings worsens the agreement with the data relative to the standard model. The strongest constraints come from the b asymmetry parameters A(b) and A(FB)(b) From a classical statistical analysis we find that the couplings lambda'(131), lambda'(132), and lambda"(321) are ruled out at the 1 sigma level, and that lambda'(133) and lambda"(33i) are ruled out at the 2 sigma level. A Bayesian statistical analysis weakens the bounds, but the corresponding chi(2)'s are uncomfortably large, rendering the relevance of the Bayesian bounds suspect.