  The production of the \chi_{c2} charmonium state in two-photon collisions has
been measured with the Belle detector at the KEKB e^+e^- collider. A clear
signal for \chi_{c2} --> \gamma J/\psi, J/\psi --> l^+l^- is observed in a
32.6fb^{-1} data sample accumulated at center-of-mass energies near 10.6GeV,
and the product of its two-photon decay width and branching fraction is
determined to be \Gamma_{\gamma\gamma}(\chi_{c2})B(\chi_{c2} --> \gamma J/\psi)
B(J/\psi --> l^+l^-)= 13.5 +/- 1.3(stat.) +/- 1.1(syst.)eV.
