  The CP-violating quark chromoelectric dipole moment (qCEDM) operator,
contributing to the electric dipole moment (EDM), mixes under renormalization
and particularly on the lattice with the pseudoscalar density. The mixing
coefficient is power-divergent with the inverse lattice spacing squared,
$1/a^2$, regardless of the lattice action used. We use the gradient flow to
define a multiplicatively renormalized qCEDM operator and study its behavior at
small flow time. We determine nonperturbatively the linearly divergent
coefficient with the flow time, $1/t$, up to subleading logarithmic
corrections, and compare it with the 1-loop perturbative expansion in the bare
and renormalized strong coupling. We also discuss the O($a$) improvement of the
qCEDM defined at positive flow time.
