  We present an experimental measurement of the refractive index of high
density Rb vapor in a gaseous atomic nanolayer. We use heterodyne
interferometry to measure the relative phase shift between two copropagating
laser beams as a function of the laser detuning and infer a peak index n = 1.26
\pm 0.02, close to the theoretical maximum of 1.31. The large index has a
concomitant large index gradient creating a region with steep anomalous
dispersion where a sub-nanosecond optical pulse is advanced by >100 ps over a
propagation distance of 390 nm, corresponding to a group index of -1x10^5, the
largest negative group index measured to date.
