First experimental results are presented from a search for events with a rapidity gap between jets. The D0 detector was used to examine events produced by the Fermilab Tevatron pp\ifmmode\bar\else\textasciimacron\fi{} collider at \ensuremath{\surd}s =1.8 TeV. The fraction of events with an observed rapidity gap between the two highest transverse energy (${\mathit{E}}_{\mathit{T}}$) jets is measured as a function of the pseudorapidity separation between the jet edges (\ensuremath{\Delta}${\mathrm{\ensuremath{\eta}}}_{\mathit{c}}$). An upper limit at the 95% confidence level of 1.1\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}2}$ is obtained on the fraction of events with non particles between the jets, for events with \ensuremath{\Delta}${\mathrm{\ensuremath{\eta}}}_{\mathit{c}}$>3 and jet ${\mathit{E}}_{\mathit{T}}$ greater than 30 GeV.