The Cryogenic Underground Observatory for Rare Events (CUORE) is a detector array comprised by 988 5cm×5cm×5cm TeO₂ crystals held below 20 mK, primarily searching for neutrinoless double-beta decay in ¹³⁰Te. 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.