Energy transfer (EnT) of near-infrared (NIR) excitons enables applications in harvesting of solar energy and biological imaging. Fast exciton extraction from NIR-absorbing Pb-chalcogenide quantum dots (QDs) may allow utilization of the photon down conversion (multiple exciton generation) process that occurs in those QDs to amplify signal in QD-based sensors or photocurrent in QD-based photovoltaics. This paper describes subnanosecond extraction of NIR excitons from PbS QDs by adsorbed J-aggregates of cyanine dye in aqueous dispersions. The QD/J-aggregate complexes form through electrostatic self-assembly, and the rate and yield of EnT within the complexes can be optimized by adjusting spectral overlap between QD emission and the J-aggregate absorption, which are controlled by density of charged ligands on the QD surface and the pH. The primary EnT pathways have rate constants ranging from (800 ps)(-1) to (2.2 ns)(-1), which are 1-2 orders of magnitude faster than previously reported examples with PbS QDs as exciton donors. The fastest EnT process occurs in 90 ps and is potentially competitive with Auger recombination of biexcitonic states in PbS QDs.