Beta-layering, the process of beta-decay heat-driven mass redistribution, has been demonstrated in a deuterium-tritium (D-T)-filled polymer sphere of the type required for fusion ignition experiments at the National Ignition Facility. This is the first report, to the best of the authors' knowledge, of a D-T layer formed in a permeation-filled sphere. The 2-mm-diam sphere was filled with D-T by permeation; cooled to cryogenic temperatures while in the high-pressure permeation vessel; and, while cold, removed to an optical axis where the D-T was frozen, melted, and beta-layered in a series of experiments over several weeks' time. This work was performed in the Los Alamos National Laboratory cryogenic pressure loader system. The beta-layering time constant was 24.0 ± 2.5 min, less than the theoretical value of 26.8 min, and not showing the significant increase due to build-up of 3He often observed in beta-layered samples. Supercooling of the liquid D-T was observed. Neither the polymer target nor its tenting material showed visual signs of degradation after 5 weeks of exposure to D-T. Small external thermal gradients were used to shift the D-T material back and forth within the sphere.