  We compute the $1/N$ correction to the location of the previously found
first-order phase transition in the Gross-Neveu model at a chemical potential
$\mu = \mu_c = {1 \over \sqrt{2}} m$, where $m$ is the fermion mass. We employ
an expression for the free energy $f(\mu)$ given by the thermodynamic Bethe
ansatz under the approximation that the fundamental fermions dominate the
ground state, and combine it with the effective potential evaluated at zero
chemical potential. Our result is $\mu_c = {m \over \sqrt{2}} [1 - {0.47 \over
N}]$.
