We report the detection of water ice in the Centaur 2060 Chiron, based on near-infrared spectra (1.0 - 2.5 micron) taken with the 3.8-meter United Kingdom Infrared Telescope (UKIRT) and the 10-meter Keck Telescope. The appearance of this ice is correlated with the recent decline in Chiron's cometary activity: the decrease in the coma cross-section allows previously hidden solid-state surface features to be seen. We predict that water ice is ubiquitous among Centaurs and Kuiper Belt objects, but its surface coverage varies from object to object, and thus determines its detectability and the occurrence of cometary activity.