GRB 000926 has one of the best-studied afterglows to-date, with multiple X-ray observations, as well as extensive multi-frequency optical and radio coverage. Broadband afterglow observations, spanning from X-ray to radio frequencies, provide a probe of the density structure of the circumburst medium, as well as of the ejecta energetics, geometry, and the physical parameters of the relativistic blastwave resulting from the explosion. We present an analysis of em Chandra X-ray Observatory observations of this event, along with em Hubble Space Telescope and radio monitoring. We combine these data with ground-based optical and IR observations and fit the synthesized afterglow lightcurve using models where collimated ejecta expand into a surrounding medium. We find that we can explain the broadband lightcurve with reasonable physical parameters only if the cooling is dominated by inverse Compton scattering. Excess X-ray emission in the broadband spectrum indicates that we are directly observing a contribution from inverse Compton scattering. It is the first time this has been observed in a GRB afterglow, and it implies that the GRB exploded in a reasonably dense (nåisebox-0.5ex 30 cm̂-3) medium, consistent with a diffuse interstellar cloud environment.