Various theories beyond the Standard Model predict new particles with masses in the sub-eV range with very weak couplings to ordinary matter. A parity-odd interaction between polarized nucleons and unpolarized matter proportional to gV gA s · p is one such possibility, where s and p are the spin and the momentum of the polarized nucleon, and gV and gA are the vector and axial vector couplings of an interaction induced by the exchange of a new light vector boson. We report a new experimental upper bound on such possible long-range parity-odd interactions of the neutron with nucleons and electrons from a recent search for parity violation in neutron spin rotation in liquid 4 He. Our constraint on the product of vector and axial vector couplings of a possible new light vector boson is gV g n A ≤ 10 −32 for an interaction range of 1m. This upper bound is more than seven orders of magnitude more stringent than the existing laboratory constraints for interaction ranges below 1m, corresponding to a broad range of vector boson masses above 10 −6 eV. More sensitive searches for a gV g n A coupling could be performed using neutron spin rotation measurements in heavy nuclei or through analysis of experiments conducted to search for nucleon-nucleon weak interactions and nuclear anapole moments.