In this article we demonstrate that PKS J1037-2705 has a weak accretion flow luminosity, well below the Seyfert 1/QSO dividing line, weak broad emission lines (BELs), and moderately powerful FR II extended radio emission. It is one of the few documented examples of a broad-line object in which the time-averaged jet kinetic luminosity, Q, is larger than the total thermal luminosity (IR to X-ray) of the accretion flow, Lbol. The blazar nucleus dominates the optical and near-ultraviolet emission and is a strong source of hard X-rays. The strong blazar emission indicates that the relativistic radio jet is presently active. The implication is that even weakly accreting AGNs can create powerful jets. Kinetically dominated (Q>Lbol) broad-line objects provide important constraints on the relationship between the accretion flow and the jet production mechanism.