K+ production far below the free nucleon-nucleon threshold has been investigated in collisions of 36Ar on 12C, natTi, and 181Ta targets at an incident energy of 92 MeV per nucleon. The cross sections for K+ production have been inferred from the observed muon decays of positive kaons. The results are discussed in the framework of a participant-spectator model and are compared to proton induced K+ production and to subthreshold pion production experiments.