The photoluminescence from a variety of individual molecules and nanometre-sized crystallites is defined by large intensity fluctuations, known as 'blinking', whereby their photoluminescence turns 'on' and 'off' intermittently, even under continuous photoexcitation. For semiconductor nanocrystals, it was originally proposed that these 'off' periods corresponded to a nanocrystal with an extra charge. A charged nanocrystal could have its photoluminescence temporarily quenched owing to the high efficiency of non-radiative (for example, Auger) recombination processes between the extra charge and a subsequently excited electron-hole pair; photoluminescence would resume only after the nanocrystal becomes neutralized again. Despite over a decade of research, completely non-blinking nanocrystals have not been synthesized and an understanding of the blinking phenomenon remains elusive. Here we report ternary core/shell CdZnSe/ZnSe semiconductor nanocrystals that individually exhibit continuous, non-blinking photoluminescence. Unexpectedly, these nanocrystals strongly photoluminesce despite being charged, as indicated by a multi-peaked photoluminescence spectral shape and short lifetime. To model the unusual photoluminescence properties of the CdZnSe/ZnSe nanocrystals, we softened the abrupt confinement potential of a typical core/shell nanocrystal, suggesting that the structure is a radially graded alloy of CdZnSe into ZnSe. As photoluminescence blinking severely limits the usefulness of nanocrystals in applications requiring a continuous output of single photons, these non-blinking nanocrystals may enable substantial advances in fields ranging from single-molecule biological labelling to low-threshold lasers.