Commensurate antiferromagnetic ordering has been observed in the superconducting high- Tc cuprate YBa2Cu3O6.5 ( Tc = 55 K) by polarized and unpolarized elastic neutron scattering. The magnetic peak intensity exhibits a marked enhancement at Tc. Zero-field muon-spin-resonance experiments demonstrate that the staggered magnetization is not truly static but fluctuates on a nanosecond time scale. These results point towards an unusual spin density wave state coexisting with superconductivity.