Allotropes of carbon, such as diamond and graphene, are among the best conductors of heat. We monitored the evolution of thermal conductivity in thin graphite as a function of temperature and thickness and found an intimate link between high conductivity, thickness, and phonon hydrodynamics. The room temperature in-plane thermal conductivity of 8.5-micrometer-thick graphite was 4300 watts per meter-kelvin-a value well above that for diamond and slightly larger than in isotopically purified graphene. Warming enhances thermal diffusivity across a wide temperature range, supporting partially hy-drodynamic phonon flow. The enhancement of thermal conductivity that we observed with decreasing thickness points to a correlation between the out-of-plane momentum of phonons and the fraction of momentum relaxing colli-1 arXiv:1910.04422v2 [cond-mat.mtrl-sci]