In recent years, it has become evident that olfaction is a fast sense, and millisecond short differences in stimulus onsets are used by animals to analyze their olfactory environment. In contrast, olfactory receptor neurons are thought to be relatively slow and temporally imprecise. These observations have led to a conundrum: how, then, can an animal resolve fast stimulus dynamics and smell with high temporal acuity? Using parallel recordings from olfactory receptor neurons in Drosophila, we found hitherto unknown fast and temporally precise odorant-evoked spike responses, with first spike latencies (relative to odorant arrival) down to 3 ms and with a SD below 1 ms. These data provide new upper bounds for the speed of olfactory processing and suggest that the insect olfactory system could use the precise spike timing for olfactory coding and computation, which can explain insects' rapid processing of temporal stimuli when encountering turbulent odor plumes.