Journal ArticleWe have looked for γ-ray emission above 100 TeV from the binary x-ray source Cygnus X-3 during a period of intense radio emission in the summer of 1989. We find no evidence for excess air showers from the direction of the source and the muon content of air showers from this direction is the same as that of ordinary cosmic rays. The flux of γ rays from Cygnus X-3 with energies exceeding 2.1x10^14 eV is < 5.5x10^-13 cm-1 sec-1 (90% C.L.)