Exclusive production of rho(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(Bj), or p(T)(2). The sin Os 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.