Total and differential cross sections for the exclusive reaction pp-->pp rho observed via the pi(+)pi(-) decay channel have been measured at p(beam)=3.67 GeV/c. The observed total meson production cross section is determined to be (23.4+/-0.8+/-8) mu b and is significantly lower than typical cross sections used in model calculations for heavy-ion collisions. The differential cross sections measured indicate a strong anisotropy (approximately cos(theta(CM)(rho)) in the rho(0) meson production.