The particle-insertion method of Widom (1963) has been widely used in numerical simulations for the purpose of calculating the excess chemical potential, mu ex. It is known, however, that values of mu ex obtained by Widom's method are strongly dependent on N, the number of particles in the system. The authors use the formalism of the grand-canonical ensemble to derive an expression for the leading term in the finite-size correction to mu ex. The new expression reduces to the exact result for hard rods and gives numerical results in good agreement with those of simulations of hard-disk and hard-sphere fluids. It is, in both respects, an improvement over an expression previously derived by Smit and Frenkel via a thermodynamic argument.