Establishing the nature of γ-ray bursts is one of the greatest challenges in high-energy astrophysics. The distribution of these bursts is isotropic across the sky, but inhomogeneous in space, with a deficit of faint bursts. It is currently unknown whether γ-ray bursts are produced in our Galaxy or at cosmological distances. The detection and identification of counterparts at other wavelengths are seen as crucial for resolving the origin of the events. Here we report the detection by the Beppo-SAX satellite of an X-ray 'afterglow', associated with the γ-ray burst of 28 February 1997 (GRB970228; ref. 3)-the first such detection for any γ-ray burst. The X-ray transient was found to contain a significant fraction of the total energy of the γ-ray burst and, following the initial detection eight hours after the main burst, faded within a few days with a power-law decay function. The rapid locating of this γ-ray burst instigated a multi-wavelength observational campaign that culminated in the identification of a fading optical transient in a position consistent with the X-ray transient reported here.