  The Cryogenic Underground Observatory for Rare Events (CUORE) is a detector
array comprised by 988 5$\;$cm$\times$5$\;$cm$\times$5$\;$cm TeO$_2$ crystals
held below 20 mK, primarily searching for neutrinoless double-beta decay in
$^{130}$Te. Unprecedented in size amongst cryogenic calorimetric experiments,
CUORE provides a promising setting for the study of exotic through-going
particles. Using the first tonne-year of CUORE's exposure, we perform a search
for hypothesized fractionally charged particles (FCPs), which are
well-motivated by various Standard Model extensions and would have suppressed
interactions with matter. No excess of FCP candidate tracks is observed over
background, setting leading limits on the underground FCP flux with charges
between $e/24-e/5$ at 90\% confidence level. Using the low background
environment and segmented geometry of CUORE, we establish the sensitivity of
tonne-scale sub-Kelvin detectors to diverse signatures of new physics.
