The two-photon width of X_(c2)^3P_2 state of charmonium has been measured using 14.4 fb^(-1) of e^+e^-data taken at √s
=9.46–11.30 GeV with the CLEO III detector. The yy-fusion reaction studied is e^+e^- → e^+e^-yy, → yy X_(c2) → yJ/Ψ → ye^+e^-(µ^+µ^-). We measure Г_(yy) (X_(c2))B(X_(c2)) → y
J/Ψ)B(J/Ψ → e^+e^- + µ^+µ^-)= 13.2 ± 1.4(stat)± 1.1(syst) eV, and obtain Г yy(Xc2)= 559 ± 57(stat) ± 48(syst) ± 36(br) eV. This result is in excellent agreement with the result of -fusion measurement by Belle and is consistent with that of the pp → X_(c2) → yy measurement, when they are both reevaluated using the recent CLEO result for the radiative decay X_(c2) → J/Ψ
