The characteristic time constants of the relaxation dynamics of core-excited atoms have hitherto been inferred from the linewidths of electronic transitions measured by continuous-wave extreme ultraviolet or X-ray spectroscopy. Here we demonstrate that a laser-based sampling system, consisting of a few-femtosecond visible light pulse and a synchronized sub-femtosecond soft X-ray pulse, allows us to trace these dynamics directly in the time domain with attosecond resolution. We have measured a lifetime of 7.9(-0.9)(+1.0) fs of M-shell vacancies of krypton in such a pump-probe experiment.