The results of a search for W boson pair production in pp¯ collisions at s=1.8TeV with subsequent decay to dilepton ( eμ,ee, and μμ) channels are presented. One event is observed with an expected background of 0.56±0.13 events with an integrated luminosity of approximately 14pb−1. Assuming equal strengths for the WWZ and WWγ gauge boson coupling parameters κ and λ, limits on the CP-conserving anomalous coupling constants are −2.6<Δκ<2.8 and −2.1<λ<2.1 at the 95% confidence level.Received 10 March 1995DOI:https://doi.org/10.1103/PhysRevLett.75.1023©1995 American Physical Society