SEMICONDUCTOR nanocrystals offer the opportunity to study the evolution of hulk materials properties as the size of a system increases from the molecular scale(1,2). In addition, their strongly size-dependent optical properties render them attractive candidates as tunable light absorbers and emitters in optoelectronic devices such as light-emitting diodes(3,4) and quantum-dot lasers(5,6), and as optical probes of biological systems(7). Here we show that light emission from single fluorescing nanocrystals of cadmium selenide under continuous excitation turns on and off intermittently with a characteristic timescale of about 0.5 seconds. This intermittency is not apparent from ensemble measurements on many nanocrystals. The dependence on excitation intensity and the change in on/off times when a passivating, high-bandgap shell of zinc sulphide encapsulates the nanocrystal(8,9) suggests that the abrupt turning off of luminescence is caused by photoionization of the nanocrystal. Thus spectroscopic measurements on single nanocrystals can reveal hitherto unknown aspects of their photophysics.