A single localized charge can quench the luminescence of a semiconductor nanowire(1), but relatively little is known about the effect of single charges on the conductance of the nanowire. In one-dimensional nanostructures embedded in a material with a low dielectric permittivity, the Coulomb interaction and excitonic binding energy are much larger than the corresponding values when embedded in a material with the same dielectric permittivity(2,3). The stronger Coulomb interaction is also predicted to limit the carrier mobility in nanowires(4). Here, we experimentally isolate and study the effect of individual localized electrons on carrier transport in InAs nanowire field-effect transistors, and extract the equivalent charge sensitivity. In the low carrier density regime, the electrostatic potential produced by one electron can create an insulating weak link in an otherwise conducting nanowire field-effect transistor, modulating its conductance by as much as 4,200% at 31 K. The equivalent charge sensitivity, 4 x 10(-5) e Hz(-1/2) at 25 K and 6 x 10(-5) e Hz(-1/2) at 198 K, is orders of magnitude better than conventional field-effect transistors(5) and nanoelectromechanical systems(6,7), and is just a factor of 20-30 away from the record sensitivity for state-of-the-art single-electron transistors operating below 4 K (ref. 8). This work demonstrates the feasibility of nanowire-based single-electron memories(9) and illustrates a physical process of potential relevance for high performance chemical sensors(10,11). The charge-state-detection capability we demonstrate also makes the nanowire field-effect transistor a promising host system for impurities (which may be introduced intentionally or unintentionally) with potentially long spin lifetimes(12,13), because such transistors offer more sensitive spin-to-charge conversion readout than schemes based on conventional field-effect transistors(13).