  The prospect of unprecedented high-quality data of gravitational waves in the
upcoming decades demands a theoretical effort to optimally study and analyze
the signals that next generation detectors will provide. Here we study the
gravitational wave emission and related dynamics during the inspiralling phase
of the Circular Restricted Three Body Problem, a modification of the
conventional binary scenario in which a small third object co-rotates with the
parent binary system. Specifically, we obtain analytic expressions for the
emitted power, frequency variation and other dynamical variables that describe
the evolution of the system. As a key highlight, we find that the presence of
the third body actually slows down the coalescence of the binary, which can be
partially interpreted as an effective rescaling of the binary's chirp-mass. Our
analysis assumes semi-Keplerian orbits for the particles and a highly mass
asymmetric parent binary needed for the stability of orbits.
