We present evidence for diffractive exclusive dijet production with an invariant dijet mass greater than 100 GeV in data collected with the DO experiment at the Fermilab Tevatron Collider. A discriminant based on calorimeter information is used to measure a significant number of events with little energy (typically less than 10 GeV) outside the dijet system, consistent with the diffractive exclusive dijet production topology. The probability for these events to be explained by other dijet production processes is 2 x 10(-6), corresponding to a 4.7 standard deviation significance.