Chemically made colloidal semiconductor quantum dots have long been proposed as scalable and color-tunable single emitters in quantum optics, but they have typically suffered from prohibitively incoherent emission. We now demonstrate that individual colloidal lead halide perovskite quantum dots (PQDs) display highly efficient single-photon emission with optical coherence times as long as 80 picoseconds, an appreciable fraction of their 210-picosecond radiative lifetimes. These measurements suggest that PQDs should be explored as building blocks in sources of indistinguishable single photons and entangled photon pairs. Our results present a starting point for the rational design of lead halide perovskite-based quantum emitters that have fast emission, wide spectral tunability, and scalable production and that benefit from the hybrid integration with nanophotonic components that has been demonstrated for colloidal materials.