We have found a new strongly correlated state of spin polarized fermions in one dimension interacting via a zero range contact interaction. We build upon the work of Lieb and Liniger who found an exact Bethe ansatz solution for one dimensional bosons interacting via a delta function interaction. Most remarkably we find that just as impenetrable bosons form a state analogous to a fermi sea, so also strongly interacting fermions form a state analogous to a bose condensate (the “fermion condensate”). The fermion condensate, like its boson counterpart, is a zero temperature superfluid (albeit an unconventional one that does not involve the formation of Cooper pairs). It may be realizable in a cold atom platform.