We present the first detection of a jet in the far-IR [O I] lines from an intermediate mass protostar. We have carried out a Herschel/PACS spectral mapping study in the [O I] lines of OMC-2 FIR 3 and FIR 4, two of the most luminous protostars in Orion outside of the Orion Nebula. The spatial morphology of the fine structure line emission reveals the presence of an extended photodissociation region (PDR) and a narrow, but intense jet connecting the two protostars. The jet seen in [O I] emission is spatially aligned with the Spitzer/IRAC 4.5 micron jet and the CO (6-5) molecular outflow centered on FIR 3. The mass loss rate derived from the total [O I] 63 micron line luminosity of the jet is 7.7 x 10^-6 M_sun/yr, more than an order of magnitude higher than that measured for typical low mass class 0 protostars. The implied accretion luminosity is significantly higher than the observed bolometric luminosity of FIR 4, indicating that the [O I] jet is unlikely to be associated with FIR 4. We argue that the peak line emission seen toward FIR 4 originates in the terminal shock produced by the jet driven by FIR 3. The higher mass-loss rate that we find for FIR 3 is consistent with the idea that intermediate mass protostars drive more powerful jets than their low-mass counterparts. Our results also call into question the nature of FIR 4.