Of all the well-localized gamma-ray bursts, GRB 000911 has the longest duration (T$_90$=500 s) and ranks in the top 1% of BATSE bursts for fluence. Here we report the discovery of the afterglow of this unique burst. In order to simultaneously fit our radio and optical observations, we are required to invoke a model involving a hard electron distribution, påisebox-0.5ex 1.5, and a jet-break time less than 1.5 days. A spectrum of the host galaxy taken 111 days after the burst reveals a single emission line, interpreted as [O II] at a redshift z=1.0585, and a continuum break that we interpret as the Balmer limit at this redshift. Despite the long T$_90$, the afterglow of GRB 000911 is not unusual in any other way when compared to the set of afterglows studied to date. We conclude that the duration of the GRB plays little part in determining the physics of the afterglow. Partially based on observations obtained at the W. M. Keck Observatory, which is operated by the California Association for Research in Astronomy, a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration.