We present the first search for pair production of isolated jets of charged leptons in association with a large imbalance in transverse energy in pp collisions using 5.8 fb⁻¹ of integrated luminosity collected by the D0 detector at the Fermilab Tevatron Collider. No excess is observed above the standard model background, and the result is used to set upper limits on the production cross section of pairs of supersymmetric chargino and neutralino particles as a function of "dark-photon" mass, where the dark photon is produced in the decay of the lightest supersymmetric particle.