  We study the secular dynamics of compact binaries (consisting of white
dwarfs, neutron stars or black holes) with tertiary companions in hierarchical
triple systems. As the inner binary (with initially negligible eccentricity)
undergoes orbital decay due to gravitational radiation, its eccentricity can be
excited by gravitational forcing from the tertiary. This excitation occurs when
the triple system passes through an "apsidal precession resonance", when the
precession rate of the inner binary, driven by the gravitational perturbation
of the external companion and general relativity, matches the precession rate
of the outer binary. The eccentricity excitation requires the outer companion
to be on an eccentric orbit, with the mutual inclination between the inner and
outer orbits less than $\sim 40^\circ$. Gravitational wave (GW) signals from
the inner binary can be significantly modified as the system evolves through
the apsidal precession resonance. For some system parameters (e.g., a white
dwarf binary with a brown dwarf tertiary), the resonance can happen when the
binary emits GWs in the $10^{-4}-10^{-1}$~Hz range (the sensitivity band of
LISA).
