The presence and distribution of hydrogen-bearing materials in meteorites are important constraints on processes in the early solar system, and the delivery of volatile constituents to growing planets. Here, we show that coordinated neutron and X-ray computed tomography, NXCT, can reveal the presence and distributions of hydrogenbearing materials in meteorites, and thus help constrain the presence and actions of water in the early solar system. NXCT is nearly nondestructive of meteorite samples. Neutron fluence in NXCT is approximately seven orders of magnitude less than in typical instrumental neutron activation analysis, and so produces little residual radioactivity and currently undetectable changes in isotope ratios. Heating during NXCT is minimal, but NXCT will overprint the record of cosmic ray exposure held in natural thermoluminescence. Two meteorites were examined. EET 87503 is a howardite, a regolith breccia inferred to be from the asteroid 4 Vesta, and contains fragments of eucrite basalt, diogenite pyroxenite, and H-rich carbonaceous chondrites. With NXCT, the chondrite fragments within the meteorite piece can be clearly located and characterized, in preparation for possible extraction and detailed analyses. Graves Nunataks (GRA) 06100 is a CR2 chondrite meteorite that contains abundant iron metal and H-bearing silicates from aqueous alteration. In NXCT, H-bearing altered material is clearly distinguished from metal, and its distribution in three dimensions is revealed as a constraint on the processes of alteration.