We present a new Monte Carlo method for estimating the chemical potential of model polymer systems. The method is based on the gradual insertion of a penetrable "ghost" polymer into the system and is effective for large chain lengths and at high densities. Insertion of the ghost chain is facilitated by use of an expanded ensemble, in which weighted transitions are permitted between states characterizing the strength of the excluded volume and thermal interactions experienced by the ghost chain. We discuss the implementation and optimization of the method within the framework of the bond fluctuation model and demonstrate its precision by a calculation of the finite-size corrections to the chemical potential.