We report the first observation of dijet production by Double Pomeron Exchange (DPE) in pbar-p collisions at sqrt(s)=1.8 TeV using the Collider Detector at Fermilab (CDF). In DPE events, large rapidity gaps, defined as a region of rapidity or pseudorapidity devoid of particles, are left in both forward directions. In a sample of events containing a leading antiproton in diffractive pbar-p interactions at sqrt(s)=1.8 TeV, we select events with at least 2 jets with transverse energy E_T>7 GeV in the kinematical region 0.035