GRB 000926 has one of the best-studied afterglows to date, with multiple X-ray observations, as well as extensive multifrequency 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 physical parameters of the relativistic blast wave resulting from the explosion. We present an analysis of Chandra X-Ray Observatory observations of this event, along with Hubble Space Telescope and radio monitoring data. We combine these data with ground-based optical and IR observations and fit the synthesized afterglow light curve using models where collimated ejecta expand into a surrounding medium. We find that we can explain the broadband light curve with reasonable physical parameters if the cooling is dominated by inverse Compton scattering. For this model, an excess due to inverse Compton scattering appears above the best-fit synchrotron spectrum in the X-ray band. No previous bursts have exhibited this component, and its observation would imply that the GRB exploded in a moderately dense (nåisebox-0.5ex 30 cm$^-3$) medium, consistent with a diffuse interstellar cloud environment.