Colloidal quantum dots exhibit efficient photoluminescence with widely tunable bandgaps as a result of quantum confinement effects(1). Such quantum dots are emerging as an appealing complement to epitaxial semiconductor laser materials, which are ubiquitous and technologically mature, but unable to cover the full visible spectrum (red, green and blue; RGB)(2). However, the requirement for high colloidal-quantum-dot packing density, and losses due to non-radiative multiexcitonic Auger recombination, have hindered the development of lasers based on colloidal quantum dots(3-9). Here, we engineer CdSe/ZnCdS core/shell colloidal quantum dots with aromatic ligands, which form densely packed films exhibiting optical gain across the visible spectrum with less than one exciton per colloidal quantum dot on average. This single-exciton gain allows the films to reach the threshold of amplified spontaneous emission at very low optical pump energy densities of 90 mu J cm(-2), more than one order of magnitude better than previously reported values(9-12). We leverage the low-threshold gain of these nanocomposite films to produce the first colloidal-quantum-dot vertical-cavity surface-emitting lasers (CQD-VCSEL). Our results represent a significant step towards full-colour single-material lasers.