  We study a two-component Bose gas with a symmetric spin-orbit coupling, and
find that two atoms can form a bound state with any intra- or inter-species
scattering length. Consequently, in the dilute limit, the
Bardeen-Cooper-Shrieffer (BCS) pairing state of bosons can be formed with
weakly-attractive inter-species and repulsive intra-species interactions. The
quasiparticle excitation energies are anisotropic due to spin-orbit coupling.
This BCS paring state is energetically favored over Bose-Einstein condensation
(BEC) of atoms at low densities. As the density increases, there is a
first-order transition from the BCS to BEC states.
