Dynamical processes are commonly investigated using laser pump-probe experiments, with a pump pulse exciting the system of interest and a second probe pulse tracking its temporal evolution as a function of the delay between the pulses. Because the time resolution attainable in such experiments depends on the temporal definition of the laser pulses, pulse compression to 200 attoseconds (1 as = 10(-18) s) is a promising recent development. These ultrafast pulses have been fully characterized, and used to directly measure light waves and electronic relaxation in free atoms. But attosecond pulses can only be realized in the extreme ultraviolet and X-ray regime; in contrast, the optical laser pulses typically used for experiments on complex systems last several femtoseconds (1 fs = 10(-15) s). Here we monitor the dynamics of ultrafast electron transfer--a process important in photo- and electrochemistry and used in solid-state solar cells, molecular electronics and single-electron devices--on attosecond timescales using core-hole spectroscopy. We push the method, which uses the lifetime of a core electron hole as an internal reference clock for following dynamic processes, into the attosecond regime by focusing on short-lived holes with initial and final states in the same electronic shell. This allows us to show that electron transfer from an adsorbed sulphur atom to a ruthenium surface proceeds in about 320 as.