The STAR collaboration reports the first observation of exclusive rho^0 photo-production, AuAu->AuAu rho^0, and rho^0 production accompanied by mutual nuclear Coulomb excitation, AuAu->Au*Au*rho^0, in ultra-peripheral heavy-ion collisions. The rho^0 have low transverse momenta, consistent with coherent coupling to both nuclei. The cross sections at sqrt(s_NN)=130GeV agree with theoretical predictions treating rho^0 production and Coulomb excitation as independent processes.