Molecular clouds around a runaway O star, zeta Oph, have been surveyed with the NANTEN telescope, and their streaming motion caused by zeta Oph has been detected. zeta Oph is the earliest (O9.5 V) member of the Sco OB 2 association and is rapidly moving accompanied by an HII region, S 27. We detected 2 major filamentary cloud complexes, L 156 and L 204 complexes. Their total masses traced by the (CO)-C-12 emission are 520 M-circle dot and 1110 M-circle dot, respectively. Denser molecular cloud cores detected in (CO)-O-18 are locally distributed on the near side of the L 204 complex to zeta Oph, and lower density gas spreads toward the opposite side. Both complexes have radial velocity shifts that are correlated with the gas density. It is suggested that the low-density gas is accelerated outward away from zeta Oph relative to the embedded dense cores. These density and velocity structures indicate a dynamical interaction between the HII region and the molecular clouds. We calculated the kinetic energies and momenta for seven individual clouds, and examined the effects of the stellar wind and photo-evaporation by the UV field of zeta Oph. It is found that the stellar wind can hardly input the momentum during the crossing time of the rapid movement of zeta Oph. UV radiation seems to be a more likely origin of the streaming gas motion.