Low mass pseudoscalars, such as the axion, can mediate macroscopic parity and time-reversal symmetry-violating forces. We searched for such a force between polarized electrons and unpolarized atoms using a novel, magnetically unshielded torsion pendulum. We improved the laboratory bounds on this force by more than 10 orders of magnitude for pseudoscalars heavier than 1 meV and have constrained this force over a broad range of astrophysically interesting masses (10 μeV to 10 meV).