Single soft-x-ray pulses of approximately 90-electron volt (eV) photon energy are produced by high-order harmonic generation with 7-femtosecond (fs), 770-nanometer (1.6 eV) laser pulses and are characterized by photoionizing krypton in the presence of the driver laser pulse. By detecting photoelectrons ejected perpendicularly to the laser polarization, broadening of the photoelectron spectrum due to absorption and emission of laser photons is suppressed, permitting the observation of a laser-induced downshift of the energy spectrum with sub-laser-cycle resolution in a cross correlation measurement. We measure isolated x-ray pulses of 1.8 (+0.7/-1.2) fs in duration, which are shorter than the oscillation cycle of the driving laser light (2.6 fs). Our techniques for generation and measurement offer sub-femtosecond resolution over a wide range of x-ray wavelengths, paving the way to experimental attosecond science. Tracing atomic processes evolving faster than the exciting light field is within reach.