  We consider the exclusive photo-production of a photon-meson pair with a
large invariant mass, working in the QCD factorisation framework. Explicitly,
we consider a $ \rho $-meson or a charged $ \pi $ in the final state. This
process gives access both to chiral-even GPDs and chiral-odd GPDs, which are
not well-known experimentally, especially the latter ones. The computation is
performed at leading order and leading twist. We discuss the prospects of
measuring them in experiments, focusing on the kinematics at the JLab 12-GeV
experiment, and pPb ultra-peripheral collisions at LHC. In particular, the
latter gives access to the small $ \xi $ regime of GPDs.
