The chemical potential of continuously deformable chain molecules can be estimated by measuring the average Rosenbluth weight associated with the virtual insertion of a molecule. We show how to generalize the overlapping-distribution method of Bennett to histograms of Rosenbluth weights. In this way we arrive at a scheme to estimate chemical potentials of chain molecules that is a direct generalization of the Shing Gubbins scheme for simple molecules. In particular, our overlapping-distribution method has the nice diagnostic feature that it can detect systematic sampling problems that may occur for long chains and high densities. We apply the method to the computation of the chemical potential of flexible chains of hard spheres and find that, for the systems studied, systematic sampling errors are less important than statistical errors.