The Spin Structure of a Polarized Photon

We show that the first moment of the spin-dependent structure function $g_1^{\gamma}(x,Q^2)$ of a real photon vanishes independent of the momentum transfer $Q^2$ it is probed with. This result is non-perturbative: it holds to all orders in perturbation theory in abelian and non-abelian gauge theory and at every twist.