  Spin precession in compact binaries is intricately tuned to the multipole
structure of the underlying bodies. For black holes, violations of the no-hair
theorems induced by modifications to general relativity correct the precession
dynamics, which in turn imprints onto the amplitude and phase modulations of
the gravitational waves emitted by the binary. Recently, the spin precession
equations were derived up to second order in spin for dynamical Chern-Simons
gravity, a parity violating modified theory of gravity. We here solve these
equations and construct, for the first time, analytic expressions for the time-
and frequency-domain gravitational waves emitted in the quasi-circular inspiral
of spin-precessing black hole binaries in a modified theory of gravity using
the post-Newtonian approximation. Working within the small coupling
approximation and using multiple scale analysis, we show that the corrections
to the nutation phase enter at relative 1PN order, and the corrections to the
precession angle and Thomas phase enter at relative 0PN order. Making use of
the stationary phase approximation and shifted uniform asymptotics, we find
that the Fourier phase of the waveform is characterized by three modifications,
two due to the back-reaction of the precession dynamics onto the spin-orbit and
spin-spin couplings that enter at 1.5PN and 2PN orders, and a 2PN modification
due to the emission of dipole radiation. We also find that back-reaction of the
precession dynamics forces the dCS corrections to the Fourier amplitude to
enter at 0PN order, as opposed to 2PN order, as expected for spin-aligned
binaries. Our work lays the first foundational stones to build an
inspiral-merger-ringdown phenomenological model for spin-precessing binaries in
a modified theory of gravity.
