A new method, called chemical potential perturbation (CPP), has been developed to predict the chemical potential as a function of density in periodic molecular simulations. The CPP method applies a spatially varying external force field to the simulation, causing the density to depend upon position in the simulation cell. Following equilibration the homogeneous (uniform or bulk) chemical potential as a function of density can be determined relative to some reference state after correcting for the effects of the inhomogeneity of the system. We compare three different methods of approximating this correction. The first method uses the van der Waals density gradient theory to approximate the inhomogeneous Helmholtz free energy density. The second method uses the local pressure tensor to approximate the homogeneous pressure. The third method uses the Triezenberg–Zwanzig definition of surface tension to approximate the inhomogeneous free energy density. If desired, the homogeneous pressure and Helmholtz free energy can also be predicted by the new method, as well as binodal and spinodal densities of a two-phase fluid region. The CPP method is tested using a Lennard-Jones (LJ) fluid at vapor, liquid, two-phase, and supercritical conditions. Satisfactory agreement is found between the CPP method and an LJ equation of state. The efficiency of the CPP method is compared to that for Widom's method under the tested conditions. In particular, the new method works well for dense fluids where Widom's method starts to fail.