Editor: M. Doser Exclusive production of ρ 0 mesons was studied at the COMPASS experiment by scattering 160 GeV/c muons off transversely polarised protons. Five single-spin and three double-spin azimuthal asymmetries were measured as a function of Q 2 , x B j , or p 2 T. The sinφ S asymmetry is found to be −0.019 ± 0.008(stat.) ± 0.003(syst.). All other asymmetries are also found to be of small magnitude and consistent with zero within experimental uncertainties. Very recent calculations using a GPD-based model agree well with the present results. The data is interpreted as evidence for the existence of chiral-odd, transverse generalized parton distributions.