Standard searches for dark matter attempt to identify interactions of dark matter particles in terrestrial detectors; a complementary search would involve looking for “dark forces,” i.e. new forces under which dark matter particles interact. In certain models of such forces, dark matter particles can obtain a tiny electric charges. Such stable “millicharged” particles can then be searched for bound in matter. We use an optical trap to measure the response to an applied electric field on a charge-neutral object that may contain such particles. This experiment has a fractional electron number sensitivity of down to 10^−4 electrons/ √ Hz regardless of the mass of the millicharged particle, allowing exploration of uncharted regions of parameter space for such dark matter candidates.