We calculate the one-loop amplitudes of the enhanced electroweak strength, O(g2M(H)2/M(W)2) or O(g2s/M(W)2), for the reaction gamma-gamma --> Z(L)Z(L), W(L)+W(L)- in the limit s, M(H)2 >> M(W)2. We find that the corresponding cross sections seem to be sufficiently large to establish a signal for the heavy Higgs boson M(H) greater-than-or-equal-to 1 TeV.