Topological insulators have been successfully identified by spin-resolved photoemission but the spin polarization remained low (~20%). We show for Bi2Te3 that the in-gap surface state is much closer to full spin polarization with measured values reaching 80% at the Fermi level. When hybridizing with the bulk it remains highly spin polarized which may explain recent unusual quantum interference results on Bi2Se3. The topological surface state shows a large circular dichroism in the photoelectron angle distribution with an asymmetry of ~20% the sign of which corresponds to that of the measured spin.