In this paper, we derive the quantum, coupled hierarchy of quark transport equations that describe the QCD plasma in the mean-field limit. The color structure of the plasma is included explicitly through non-Abelian interactions, and the dynamical structure of the quark component fully respects gauge covariance. A new gluon Wigner operator and its associated momentum moments are introduced and discussed. We also discuss the future application of our nonequilibrium truncation scheme to this coupled hierarchy of equations.