The high-speed, high-accuracy transport of single electrons in nanoscale devices is predicted to underpin future electronics. A key and topical application is the development of a fundamental standard of electrical current linking the ampere to the elementary charge and frequency. For a practical standard, currents at the nanoampere level are required, corresponding to gigahertz transport frequencies. Recent research has concentrated on transport using Coulomb blockade techniques. However, the tunnelling time of the electrons in such devices limits the operation to a few megahertz. We present a different pumping mechanism of single charges, whereby electrons ‘surf’ as particles on a time-dependent potential instead of tunnelling through the barriers as waves. This potential is created by two phase-shifted sinusoidal signals applied directly to metallic finger gates on an etched GaAs/AlGaAs quantum wire. Pumping accurate to better than 10−4, at a frequency up to 3.4 GHz, is reported with this approach.