Rare Pionium Decays and Pion Polarizability

We calculate the decay of pionium atoms into two photons. The pion polarizability gives rise to a 10% correction to the corresponding decay width for pointlike pions. This opens the possibility to obtain the difference between the electric and magnetic polarizability of the charged pion from a future measurement of the branching fraction of pionium into two photons. For such an experiment the \pi\pi-scattering lengths would have to be known to better than 5% precision. We also comment on the contribution of the axial anomaly to the decay of pionium into \gamma\pi^0.