We have performed a search at the Bevatron for the decays KL0-->μ+μ- ,e+e- , and μ+/-e-/+ with a double magnetic spectrometer using wire spark chambers. Over 106 observed KL0-->π+π- decays determine the normalization for the di-lepton decay modes. No e+e- or μ+/-e-/+ events were observed. For each of these decays the upper limit on the branching ratio relative to all modes is 1.57 × 10-9 (90% confidence level). For the decay KL0-->μ+μ-, the limit is 1.82 × 10-9 (90% confidence level).