We propose a method to generate an isolated single-cycle pulse in the extreme-ultraviolet spectral region using a broadband conventional laser. The uncompressed laser pulse imprints a chirped sinusoid current profile onto a relativistic electron beam. As the beam propagates along a specifically tailored magnetic field of an undulator, it produces an isolated single-cycle pulse. For moderate laser intensities (0.2 mJ per pulse) and typical operating parameters of current electron accelerators, we predict a 26 as, 5 GW peak-power pulse spanning wavelengths down to 15 nm.