We report the first measurement of the differential cross section for the process γγ→ηη in the kinematic range above the ηη threshold, 1.096 GeV<W<3.8 GeV over nearly the entire solid angle range, |cos⁡θ*|≤0.9 or ≤1.0 depending on W, where W and θ* are the energy and η scattering angle, respectively, in the γγ 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/c2 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 χcJ charmonia.