A sensitive search for the lepton-number-violating decay Ξ-→pμ-μ- has been performed using a sample of ∼109Ξ- hyperons produced in 800GeV/c p-Cu collisions. We obtain B(Ξ-→pμ- μ-)<4.0×10-8 at 90% confidence, improving on the best previous limit by 4 orders of magnitude. © 2005 The American Physical Society.