  While the chiral-even content of the nucleon is better and better studied,
the chiral-odd transversity generalized parton distributions (GPDs) remain
almost unknown. These GPDs can be accessed experimentally through the exclusive
photoproduction process gamma + N -> pi + rho + N', in the kinematics where the
meson pair has a large invariant mass and the final nucleon has a small
transverse momentum, provided the vector meson is produced in a transversally
polarized state. We calculate perturbatively the scattering amplitude at
leading order in alpha_s. We build a simple model for the dominant transversity
GPD H_T(x,xi,t) based on the concept of double distribution. We estimate the
unpolarized differential cross section for this process in the kinematics of
the Jlab and COMPASS experiments. Counting rates show that the experiment looks
feasible with the real and quasi real photon beam characteristics expected at
JLab@12 GeV, and with the quasi real photon beam in the COMPASS experiment.
