A recently devised method of establishing arbitrarily close upper and lower bounds on the chemical potential for certain kinds of thermodynamic systems is applied to a one-dimensional lattice system whose sites cannot accept particles as nearest neighbors, i.e., whose particles repel one another when they are nearest neighbors. The exact chemical potential is found to always lie within the bounds, and the convergence of the bounds is examined for lattices of increasing size. The system, of course, lacks a phase transition, but its study, which is both brief and simple, is useful for the purposes of illustration and completeness.