  The \textsc{Majorana Demonstrator} is an ultra low-background experiment
searching for neutrinoless double-beta decay in $^{76}$Ge. The heavily shielded
array of germanium detectors, placed nearly a mile underground at the Sanford
Underground Research Facility in Lead, South Dakota, also allows searches for
new exotic physics. Free, relativistic, lightly-ionizing particles with
electrical charges less than $e$ are forbidden by the standard model but
predicted by some of its extensions. If such particles exist, they might be
detected in the \textsc{Majorana Demonstrator} by searching for multiple-
detector events with individual-detector energy depositions down to 1 keV. This
search is background free and no candidate events have been found in 285 days
of data taking. New direct-detection limits are set for the flux of lightly
ionizing particles for charges as low as $e$/1000.
