  We report the first measurement of the differential cross section for the
process gamma gamma --> eta eta in the kinematic range above the eta eta
threshold, 1.096 GeV < W < 3.8 GeV over nearly the entire solid angle range,
|cos theta*| <= 0.9 or <= 1.0 depending on W, where W and theta* are the energy
and eta scattering angle, respectively, in the gamma gamma center-of-mass
system. The results are based on a 393 fb^{-1} data sample collected with the
Belle detector at the KEKB e^+ e^- collider. In the W range 1.1-2.0 GeV/c^2 we
perform an analysis of resonance amplitudes for various partial waves, and at
higher energy we compare the energy and the angular dependences of the cross
section with predictions of theoretical models and extract contributions of the
chi_{cJ} charmonia.
