  We employ inelastic light scattering with magnetic fields to study
intersubband spin plasmons in a quantum well. We demonstrate the existence of a
giant collective spin-orbit (SO) field that splits the spin-plasmon spectrum
into a triplet. The effect is remarkable as each individual electron would be
expected to precess in its own momentum-dependent SO field, leading to
D'yakonov-Perel' dephasing. Instead, many-body effects lead to a striking
organization of the SO fields at the collective level. The macroscopic spin
moment is quantized by a uniform collective SO field, five times higher than
the individual SO field. We provide a momentum-space cartography of this field.
