  We present a calculation of the renormalized HQET Lagrangian at order
O(1/m_Q^3) in the one particle sector. The anomalous dimensions of local
operators and time ordered products of dimension 7 contributing at this order
are calculated in the one loop approximation. We show that a careful treatment
of the time ordered products is necessary to arrive at a gauge independent
renormalized lagrangian. Our result sets the stage for an investigation of
reparametrization invariance at O(1/m_Q^3).
