Several planetary satellites apparently have subsurface seas that are of great interest for, among other reasons, their possible habitability. The geologically diverse saturnian satellite Enceladus vigorously vents liquid water and vapor from fractures within a south polar depression and thus must have a liquid reservoir or active melting. However, the extent and location of any subsurface liquid region is not directly observable. We use measurements of control points across the surface of Enceladus accumulated over seven years of spacecraft observations to determine the satellite's precise rotation state, finding a forced physical libration of 0.120 ± 0.014° (2σ). This value is too large to be consistent with Enceladus's core being rigidly connected to its surface, and thus implies the presence of a global ocean rather than a localized polar sea. The maintenance of a global ocean within Enceladus is problematic according to many thermal models and so may constrain satellite properties or require a surprisingly dissipative Saturn.