We perform a perturbative analysis of the effective action, as defined in the paper, of quantum chiral W3 gravity. The results are given as a 1/c expansion, where c is the central charge of the matter system that drives the W3 gravity dynamics. Certain nonlocalities in the Ward identities for the induced action, which we found previously, are cancelled by 1-loop contributions from propagating spin-2 and spin-3 gauge fields, On the basis of these results, we propose an exact all-order result for the effective action.