  We derive the order $p^8$ Lagrangian of odd intrinsic parity for mesonic
chiral perturbation theory, and provide the resulting operator basis in the
supplementary material. Neglecting the non-zero singlet trace, we find $999$
operators for a general number of quark flavours $N_f$, $705$ for $N_f=3$ and
$92$ for $N_f=2$. Our numbers agree with those obtained through the Hilbert
series approach in the literature. Including a singlet trace, as needed for the
physical case of $N_f=2$, instead yields $1210$ operators for a general $N_f$,
$892$ for $N_f=3$ and $211$ for $N_f=2$.
