Is the neutron round? And why do we care? It turns out that the neutron’s electric dipole moment (EDM) is surprisingly small; in other words the neutron is surprisingly round. Far from being an obscure footnote, the small value of the neutron EDM has possible implications for the nature of dark matter, and may provide information on the mechanism responsible for the existence of any matter at all following the Big Bang. This talk will provide a brief introduction to the relationship between EDM measurements and these scientific questions and will describe an approach our collaboration is pursuing with a goal of improving the neutron EDM measurement precision by two orders of magnitude.