We report the observation and measurement of the rate of diffractive dijet production at the Fermilab Tevatron ¯pp collider at √s=1.8TeV. In events with two jets of ET>20GeV, 1.8<|η|<3.5, and η1η2>0, we find that the diffractive to nondiffractive production ratio is RJJ=[0.75±0.05(stat)±0.09(syst)]%. By comparing this result, in combination with our measured rate for diffractive W boson production reported previously, with predictions based on a hard partonic pomeron structure, we determine the pomeron gluon fraction to be fg=0.7±0.2.