The interactions of hydrogen with ceria have been the subject of several experimental studies, but whether hydrogen atoms enter the bulk or are merely chemisorbed on the surfaces is disputed. We combine first-principles calculations with thermodynamic arguments and conclude that the uptake of small amounts of hydrogen by ceria is spontaneous below 665 K. The calculations also predict that hydrogen atoms within the bulk form hydroxyl groups and slightly expand the lattice. The predicted hydrogen content, OH vibrational frequency, and ceria lattice expansion upon hydrogen uptake are consistent with available data.