Aerogel materials have myriad scientific and technological applications due to their large intrinsic surface areas and ultralow densities. However, creating a nanodiamond aerogel matrix has remained an outstanding and intriguing challenge. Here we report the high-pressure, high-temperature synthesis of a diamond aerogel from an amorphous carbon aerogel precursor using a laser-heated diamond anvil cell. Neon is used as a chemically inert, near-hydrostatic pressure medium that prevents collapse of the aerogel under pressure by conformally filling the aerogel's void volume. Electron and X-ray spectromicroscopy confirm the aerogel morphology and composition of the nanodiamond matrix. Time-resolved photoluminescence measurements of recovered material reveal the formation of both nitrogen- and silicon- vacancy point-defects, suggesting a broad range of applications for this nanocrystalline diamond aerogel.