  The chiral-odd generalized parton distribution (GPD), or transversity GPD, of
the nucleon can be accessed experimentally through the photo- or
electroproduction of two vector mesons on a polarized nucleon target,
\gamma^(*) N --> \rho_1 \rho_2 N', where \rho_1 is produced at large transverse
momentum, \rho_2 is transversely polarized, and the mesons are separated by a
large rapidity gap. We predict the cross section for this process for both
transverse and longitudinal \rho_{2} production. To this end we propose a model
for the transversity GPD H_T(x,\xi,t), and give an estimate of the relative
sizes of the transverse and longitudinal \rho_{2} cross sections. We show that
a dedicated experiment at high energy should be able to measure the
transversity content of the proton.
