Widespread deployment of multicast depends on the existence of congestion control protocols that are provably fair to unicast traffic. In this work, we present an optimization-based congestion control mechanism for single-rate multicast communication with provable fairness properties. The optimization-based approach attempts to find an allocation of rates that maximizes the aggregate utility of the network. We show that the utility of multicast sessions must be carefully defined if a widely accepted property of aggregate utility is to hold. Our definition of session utility amounts to maximizing a weighted sum of simple utility functions, with weights determined by the number of receivers. The fairness properties of the optimal rate allocation depend both on the weights and form of utility function used. We present analysis for idealized topologies showing that while our mechanism is not strictly fair to unicast, its unfairness can be controlled by appropriate choices of parameters.