A key step in the origin of life is the establishment of autocatalytic cycles controlled by biopolymer catalysts. These catalysts (either ribozymes or proteins) are composed of homochiral monomers. Homochirality in living systems is maintained because biopolymers are asymmetric in their catalysis and synthesize molecules of their own handedness. Asymmetric autocatalysis is also possible with small molecules, as demonstrated by the Soai reaction, but it is rare. As far as we know, single nucleotides and amino acids are not autocatalytic. The observation that organic molecules in meteorites can have an enantiomeric excess of a few percent suggests that the prebiotic mixture may have had a partial chiral bias that was caused by external physical influences. Here, we consider the way that such a partial prebiotic bias would influence the origin of ribozymes in an RNA world scenario. We have previously shown how a transition to a living state can occur in a model for RNA polymerization. Here, we add chirality to the problem by considering simultaneous synthesis and polymerization of left- and right-handed monomers. The two chemical synthesis rates may be equal or unequal, due to physical or chemical effects prior to the origin of life. We determine the stationary states of this reaction system. The nonliving state is racemic, or slightly biased. There are two living states that are almost completely homochiral, whether or not the nonliving state is biased. It is a feature of our model that, for some regions of parameter space, living and nonliving states are both found to be stable under the same conditions. The origin of life therefore involves a stochastic transition between the nonliving and living states. Our model extends previous theories by treating the origin of life and the origin of chirality as aspects of the same model.