We report on a neutron particle physics experiment, which provides for the first time an upper limit on the strength of an axial coupling constant for a new light spin 1 boson in the millimeter range. Such a new boson would mediate a new force between ordinary fermions, like neutrons and protons. The experiment was set up at the cold neutron reflectometer Narziss at the Paul Scherrer Institute and uses Ramsey's technique of separated oscillating fields to search for a pseudomagnetic neutron spin precession induced by this new interaction. For the axial coupling constant g(A)(2), an upper limit of 6×10(-13) (95% C.L.) was determined for an interaction range of 1 mm.