Inclusive dijet production at large pseudorapidity intervals (Δη)between the two jets has been suggested as a regime for observing Balitsky-Fadin-Kuraev-Lipatov (BFKL) dynamics. We have measured the dijet cross section for large Δη in pp¯ collisions at √s = 1800 and 630 GeV using the D0 detector. The partonic cross section increases strongly with the size of Δη. The observed growth is even stronger than expected on the basis of BFKL resummation in the leading logarithmic approximation. The growth of the partonic cross section can be accommodated with an effective BFKL intercept of αBFKL = 1.65 ±0.07.