  We present the first calculation of the jet transport coefficient $\hat{q}$
in quenched and (2+1)-flavor QCD on a 4-D Euclidean lattice. The light-like
propagation of an energetic parton is factorized from the mean square gain in
momentum transverse to the direction of propagation, which is expressed in
terms of the thermal field-strength field-strength correlator. The
leading-twist term in its operator product expansion is calculated on the
lattice. Continuum extrapolated quenched results, and full QCD estimates based
on un-renormalized lattice data, over multiple lattice sizes, are compared with
(non) perturbative calculations and phenomenological extractions of $\hat{q}$.
The lattice data for $\hat{q}$ show a temperature dependence similar to the
entropy density. Within uncertainties, these are consistent with
phenomenological extractions, contrary to calculations using perturbation
theory.
