Abstract
Dynamical Chern-Simons (DCS) gravity, a typical parity-violating gravitational theory, modifies both the generation and propagation of gravitational waves from general relativity (GR). In this work, we derive the gravitational waveform radiated from a binary slowly-rotating black hole system with eccentric orbits under the spin-aligned assumption in the DCS theory. Compared with GR, DCS modification enters the second-order post-Newtonian (2PN) approximation, affecting the spin-spin coupling and monopole-quadrupole coupling of binary motion. This modification produces an extra precession rate of periastron. This effect modulates the scalar and gravitational waveform through a quite low frequency. Additionally, the dissipation of conserved quantities results in the secular evolution of the semimajor axis and the eccentricity of binary orbits. Finally, the frequency-domain waveform is given in the post-circular scheme, requiring the initial eccentricity to be ≲ 0.3. This ready-to-use template will benefit the signal searches and improve the future constraint on DCS theory.