  We discuss the construction of the most general CP-violating chiral
Lagrangian for an axion-like particle (ALP). Starting with an effective
Lagrangian containing light quarks and gluons, we provide its matching onto a
chiral effective Lagrangian at $\mathcal{O}(p^2)$ described in terms of mesons
and baryons, identifying the correspondence between the Jarlskog invariants of
the two theories. After deriving the ALP interactions with mesons and baryons,
we analyse a few relevant phenomenological implications such as the permanent
electric dipole moments of nucleons and the CP-violating ALP and kaon
decays.This work provides the necessary tools for further phenomenological
analyses connecting low-energy observables with the couplings of the underlying
ultraviolet complete theory.
