We present a search for a neutral, long-lived particle L that is produced in e+ e- collisions and decays at a significant distance from the e+ e- interaction point into various flavor combinations of two oppositely charged tracks. The analysis uses an e+ e- data sample with a luminosity of 489.1 fb(-1) collected by the BABAR detector at the ϒ(4S), ϒ(3S), and ϒ(2S) resonances and just below the ϒ(4S). Fitting the two-track mass distribution in search of a signal peak, we do not observe a significant signal, and set 90% confidence level upper limits on the product of the L production cross section, branching fraction, and reconstruction efficiency for six possible two-body L decay modes as a function of the L mass. The efficiency is given for each final state as a function of the mass, lifetime, and transverse momentum of the candidate, allowing application of the upper limits to any production model. In addition, upper limits are provided on the branching fraction B(B→XsL), where Xs is a strange hadronic system.