First-principles density functional calculations demonstrate that a spin-polarized two-dimensional conducting state can be realized at the interface between two non-magnetic band insulators. The (001) surface of the diamagnetic insulator FeS2 (pyrite) supports a localized surface state deriving from Fe d-orbitals near the conduction band minimum. The deposition of a few unit cells of the polar perovskite oxide LaAlO3 leads to electron transfer into these surface bands, thereby creating a conducting interface. The occupation of these narrow bands leads to an exchange splitting between the spin sub-bands, yielding a highly spin-polarized conducting state distinct from the rest of the non-magnetic, insulating bulk. Such an interface presents intriguing possibilities for spintronics applications.