Hadron pair production gamma gamma --> h (h) over bar in the region where the c.m. energy is much smaller than the photon virtuality can be described in a factorized form, as the convolution of a partonic handbag diagram and generalized distribution amplitudes which are new nonperturbative functions describing the exclusive fragmentation of a quark-antiquark pair into two hadrons. Scaling behavior and a selection rule on photon helicity an signatures of this mechanism. The case where h is a pion is emphasized.