We present results from Experiment E917 for antilambda and antiproton production in Au+Au collisions at 11.7 A GeV. We have measured invariant spectra and yields for both species in central and peripheral collisions. We find that the antilambda/antiproton ratio near mid-rapidity increases from 0.26+0.19-0.15 in peripheral collisions to 3.6+4.7-1.8 in central collisions, a value that is substantially larger than current theoretical estimates.