  We study the process $\gamma \gamma \to J/\psi \omega$ using a data sample of
519.2 $fb^{-1}$ recorded by the BaBar detector at SLAC at the PEP-II
asymmetric-energy $e^+ e^-$ collider at center-of-mass energies near the
$\Upsilon(nS)$ ($n = 2,3,4$) resonances. We confirm the existence of the
charmonium-like resonance X(3915) decaying to $J/\psi \omega$ with a
significance of 7.6 standard deviations, including systematic uncertainties,
and measure its mass $(3919.4 \pm 2.2 \pm 1.6) MeV/c^2$ and width $(13 \pm 6
\pm 3) MeV$, where the first uncertainty is statistical and the second
systematic. A spin-parity analysis supports the assignment $J^P=0^+$ and
therefore the identification of the signal as due to the $\chi_{c0}(2P)$
resonance. In this hypothesis we determine the product between the two-photon
width and the final state branching fraction to be $(52 \pm 10 \pm 3) eV$
