Using the ZEUS detector at the HERA electronproton collider, we have searched for lepton flavor violation in ep collisions at a center—of—mass energy ($sqrt S$) of 300 GeV. Events of the type e + p → ℓ + X with a final—state lepton of high transverse momentum, ℓ = μ or τ, were sought. No evidence was found for lepton flavor violation in the combined 1993 and 1994 data samples, for which the integrated luminosities were 0.84 pb{−1}for e{∼p collisions and 2.94 pb{−1} for e+p collisions. Limits on coupling vs. mass are provided for leptoquarks and R—parity violating squarks. For flavor violating couplings of electromagnetic strength, we set 95% confidence level lower limits on leptoquark masses between 207 GeV and 272 GeV, depending on the leptoquark species and final—state lepton. For leptoquark masses larger than 300 GeV, limits on flavor—changing couplings are determined, many of which supersede prior limits from rare decay processes.