The highly localized acceleration of electrons at the foreshock reported by Anderson et al. (1979) is explained in terms of a fast Fermi process. The basic notion is that in the solar wind frame the nearly perpendicular bow shock at the point of tangency of the interplanetary magnetic field acts as a fast-moving magnetic mirror which can reflect electrons with sufficiently large pitch angles. The reflection process can effectively energize electrons and drive them upstream. If the seed electrons have energies of several hundred electron volts, they can attain energies of several keV through the acceleration process.