A search has been made for the production of a charmonium state chi-c2 in two-photon processes. We have used the decay channel chi-c2 --> gamma-J/chi, J/chi --> l + l-. No signal enhancement indicating the production of chi-c2 has been observed in the invariant mass distributions of the final state particles, and an upper limit for the two-photon decay width, GAMMA-gamma-gamma(chi-c2) < 4.2 keV at 95% CL, has been obtained.