  We propose and formulate an interaction induced staggered spin-orbit order as
a new emergent phase of two-dimensional Fermi gases. We show that when some
form of inherent spin-splitting via Rashba-type spin-orbit coupling renders two
helical Fermi surfaces to become significantly `nested', a Fermi surface
instability arises. To lift this degeneracy, a spontaneous symmetry breaking
spin-orbit density wave develops, causing a surprisingly large quasiparticle
gapping with chiral electronic states. Since the staggered spin-orbit order is
associated with a condensation energy, quantified by the gap value, destroying
such spin-orbit interaction costs sufficiently large perturbation field or
temperature or de-phasing time. BiAg$_2$ surface state is shown to be a
representative system for realizing such novel spin-orbit interaction with
tunable and large strength, and the spin-splitting is decoupled from charge
excitations. These functional properties are relevant for spin-electronics,
spin-caloritronics, and spin-Hall effect applications.
