We present results from a measurement of double diffraction dissociation in p¯p collisions at the Fermilab Tevatron collider. The production cross section for events with a central pseudorapidity gap of width Δη0>3 (overlapping η=0) is found to be 4.43±0.02(stat)±1.18(syst)mb [ 3.42±0.01(stat)±1.09(syst)mb] at s√=1800[630]GeV. Our results are compared with previous measurements and with predictions based on Regge theory and factorization.