We study the gauge-fixing approach to the construction of lattice chiral gauge theories in one-loop weakcoupling perturbation theory. We show how the infrared properties of the gauge degrees of freedom determine the nature of the continuous phase transition at which we take the continuum limit. The fermion self-energy and the vacuum polarization are calculated, and confirm that, in the Abelian case, this approach can be used to put chiral gauge theories on the lattice in four dimensions. We comment on the generalization to the non-Abelian case. ͓S0556-2821͑98͒00415-9͔