In this paper we apply two independent methods to determine chemical potentials locally, the overlapping distribution method of Shing and Gubbins and thermodynamic integration from an Einstein crystal, to the same Monte Carlo simulation. The system is a Lennard-Jones crystal with a surface near the melting point. We demonstrate that the overlapping distribution method results in reliable free energies in the surface region, whereas thermodynamic integration is preferable for the bulk part of the system. In this way we succeeded to check, for the first time, chemical equilibrium between surface and bulk. Such a consistency check is essential whenever one uses Monte Carlo or molecular dynamics simulations to study equilibrium properties of crystal surfaces, since relaxation times easily exceed acceptable simulation times.