We present a new definition of the jet quenching parameter $\hat{q}$ in a weakly-coupled quark-gluon plasma undergoing boost-invariant longitudinal expansion. We propose a boost-invariant definition of $\hat{q}$, which is proportional to the broadening of the angular variables $\eta$ (the pseudo-rapidity) and $\phi$ (the azimuthal angle). We furthermore consider radiative corrections to $\hat{q}$ and find potentially large corrections enhanced by a double logarithm like the case of a static medium. But unlike for the static medium, these corrections are now local in (proper) time.}