We report results of the first measurements of Λ and Λ̄ polarization produced in deep inelastic polarized muon scattering on the nucleon. The results are consistent with an expected trend towards positive polarization with increasing cursive Greek chiF. The polarizations of Λ and Λ̄ appear to have opposite signs. A large negative polarization for Λ at low positive cursive Greek chiF is observed and is not explained by existing models. A possible interpretation is presented.