Spin polarization and dispersion of the L-gap surface states on Au(111) are investigated theoretically by means of first-principles electronic-structure and photoemission calculations. In analogy to a two-dimensional electron gas, spin-orbit coupling results in a large in-plane spin polarization. A small component normal to the surface is reported for the first time. The photoelectron spin can differ considerably from that of the initial surface states, e.g. depending on light polarization and detection azimuth.