In the standard model of particle physics, the weak interaction is described by vector and axial-vector couplings only. Nonzero scalar or tensor interactions would imply an additional contribution to the differential decay rate of the neutron, the Fierz interference term. We derive a limit on this hypothetical term from a measurement using spin-polarized neutrons. This method is statistically less sensitive than the determination from the spectral shape but features much cleaner systematics. We obtain a limit of b=0.017(21) at 68.27% C.L., improving the previous best limit from neutron decay by a factor of four.