Short duration (<2 s) Gamma-ray bursts (GRBs) have been a mystery since their discovery. Until May 2005 very little was known about short GRBs, but this situation has changed rapidly in the last few months since the Swift and HETE-2 satellites have made it possible to discover X-ray and optical counterparts to these sources. Positional associations indicate that short GRBs arise in close-by galaxies (z<0.7). Here we report on a detailed study of the short GRB 050724 X-ray afterglow. This burst shows strong flaring variability in the X-ray band. It clearly confirms early suggestions of X-ray activity in the 50-100 s time interval following the GRB onset seen with BATSE. Late flare activity is also observed. These observations support the idea that flares are related to the inner engine for short GRBs, as well as long GRBs.