  We present the first observation and cross section measurement of exclusive
dijet production in pbar-p interactions, pbar + p --> pbar + dijet + p. Using a
data sample of 310 pb-1 collected by the Run II Collider Detector at Fermilab
at sqrt{s}=1.96 TeV, exclusive cross sections for events with two jets of
transverse energy ET >= 10 GeV have been measured as a function of minimum
ET(jet). The exclusive signal is extracted from fits to data distributions
based on Monte Carlo simulations of expected dijet signal and background
shapes. The simulated background distribution shapes are checked in a study of
a largely independent data sample of 200 pb-1 of b-tagged jet events, where
exclusive dijet production is expected to be suppressed by the Jz=0 total
angular momentum selection rule. Results obtained are compared with theoretical
expectations, and implications for exclusive Higgs boson production at the pp
Large Hadron Collider at sqrt{s}=14 TeV are discussed.
