We report a measurement of the fraction of events with a large pseudorapidity gap Δη within the pseudorapidity region available to the proton dissociation products X in p¯+p→p¯+X. For a final state p¯ of fractional momentum loss ξp¯ and 4-momentum transfer squared tp¯ within 0.06<ξp¯<0.09 and |tp¯|<1.0 [0.2] GeV2 at s√=1800 [630] GeV, the fraction of events with Δη>3 is found to be 0.246±0.001 (stat)±0.042 (syst) [0.184±0.001 (stat)±0.043 (syst)]. Our results are compared with gap fractions measured in minimum bias p¯p collisions and with theoretical expectations.