We present the results of a search for the decay B0-->tau+tau- in a data sample of (232+/-3)x10(6) Upsilon(4S)-->BB decays using the BABAR detector. Certain extensions of the standard model predict measurable levels of this otherwise rare decay. We reconstruct fully one neutral B meson and seek evidence for the signal decay in the rest of the event. We find no evidence for signal events and obtain Beta(B0->tau+tau-)<4.1x10(-3) at the 90% confidence level.