We performed high-resolution spin- and angle-resolved photoemission spectroscopy studies of the electronic structure and the spin texture on the surface of Bi2Se3, a model TI. By tuning the photon energy, we found that the topological surface state is well separated from the bulk states in the vicinity of kz = Z plane of the bulk Brillouin zone. The spin-resolved measurements in that region indicate a very high degree of spin polarization of the surface state, ~0.75, much higher than previously reported. Our results demonstrate that the topological surface state on Bi2Se3 is highly spin polarized and that the dominant factors limiting the polarization are mainly extrinsic.