  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.
