Previously proposed mechanisms have difficulty explaining the disruption of Comet C/2012 S1 (ISON) as it approached the Sun. We describe a novel cometary disruption mechanism whereby comet nuclei fragment and disperse through dynamic sublimation pressure, which induces differential stresses within the interior of the nucleus. When these differential stresses exceed its material strength, the nucleus breaks into fragments. We model the sublimation process thermodynamically and propose that it is responsible for the disruption of Comet ISON. We estimate the bulk unconfined crushing strength of Comet ISON's nucleus and the resulting fragments to be 0.5 Pa and 1-9 Pa respectively, assuming typical Jupiter Family Comet (JFC) albedos. However, if Comet ISON has an albedo similar to Pluto, this strength estimate drops to 0.2 Pa for the intact nucleus and 0.6-4 Pa for its fragments. Regardless of assumed albedo, these are similar to previous strength estimates of JFCs. This suggests that, if Comet ISON is representative of dynamically new comets, then low bulk strength is a primordial property of some comet nuclei, and not due to thermal processing during migration into the Jupiter Family. ; Comment: 37 pages, 4 figures