  We derive spin-orbit coupling effects on the gravitational field and
equations of motion of compact binaries in the 2.5 post-Newtonian approximation
to general relativity, one PN order beyond where spin effects first appear. Our
method is based on that of Blanchet, Faye, and Ponsot, who use a post-Newtonian
metric valid for general (continuous) fluids and represent pointlike compact
objects with a delta-function stress-energy tensor, regularizing divergent
terms by taking the Hadamard finite part. To obtain post-Newtonian spin
effects, we use a different delta-function stress-energy tensor introduced by
Bailey and Israel. In a future paper we will use the 2.5PN equations of motion
for spinning bodies to derive the gravitational-wave luminosity and phase
evolution of binary inspirals, which will be useful in constructing matched
filters for signal analysis. The gravitational field derived here may help in
posing initial data for numerical evolutions of binary black hole mergers.
