The scalar version of the Aharonov-Bohm effect predicts a phase shift for de Broglie waves due to the action of a scalar potential in an otherwise field-free (i.e. force-free) region of space. Unlike the more familiar effect due to the magnetic vector potential, the scalar effect has hitherto remained unverified due, presumably, to technical difficulties in electron interferometry. Rather than using electrons acted on by electrostatic potentials, an analogous interferometry experiment was performed with thermal neutrons subject to pulsed magnetic fields. The observations were carried out at the Missouri University Research Reactor, using a skew-symmetric perfect silicon crystal neutron interferometer. The expected phase shifts have been observed to a high degree of accuracy. 7 refs., 4 figs.