  We study deeply virtual Compton scattering on a virtual pion that is emitted
by a proton. Using a range of models for the generalized parton distributions
of the pion, we evaluate the cross section, as well as the beam spin and beam
charge asymmetries in the leading-twist approximation. Studying Compton
scattering on the pion in suitable kinematics puts high demands on both beam
energy and luminosity, and we find that the corresponding requirements will
first be met after the energy upgrade at Jefferson Laboratory. As a by-product
of our study, we construct a parameterization of pion generalized parton
distributions that has a non-trivial interplay between the x and t dependence
and is in good agreement with form factor data and lattice calculations.
