We describe the process $\gamma N → \gamma \rho N′$ in the generalized Bjorken regime where the $\gamma \rho$ pair has a
large invariant mass. In the collinear QCD factorization framework, the amplitude gives access to both chiral-even and chiral-odd quark generalized parton distributions (GPDs), and is insensitive to gluon GPDs. The separation of longitudinally and transversely polarized $\rho$ meson production allows to distinguish chiral-even and chiral-odd contributions. Production rates are estimated in the kinematics of the near-future JLab 12-GeV experiments.