  We describe a new kind of resonance occuring in relativistic three-body
hierarchical systems: the precession resonance, occuring when the relativistic
precession timescale of a binary equals the period of a distant perturber. We
find that, contrary to what most previous studies assume, it can lead to an
exponential increase of eccentricity of the binary even when relativistic
precession dominates the quadrupolar perturbation. The resonance may happen in
the observation band of LISA or change the eccentricity distribution of
triples. We discuss the physics of the resonance, showing that it mainly
depends on three parameters.
