We report measurements of electrical transport through single CdSe/CdS core/shell colloidal quantum dots (cQDs) connected to source and drain contacts. We observe telegraphic switching noise showing few plateaus at room temperature. We model and interpret these results as charge trapping of individual trap states, and therefore we resolve individual charge defects in these high-quality low-strain cQDs. The small number of observed defects quantitatively validates the passivation method based on thick CdS shells nearly lattice-matched to CdSe cores first developed to suppress photoluminescence blinking. Finally, we introduce a figure of merit useful to efficiently distinguish telegraphic noise from noise with a Gaussian distribution.