  In this work we show that with high probability the chromatic number of a
graph sampled from the random regular graph model $\Gnd$ for $d=o(n^{1/5})$ is
concentrated in two consecutive values, thus extending a previous result of
Achlioptas and Moore. This concentration phenomena is very similar to that of
the binomial random graph model $\Gnp$ with $p=\frac{d}{n}$. Our proof is
largely based on ideas of Alon and Krivelevich who proved this two-point
concentration result for $\Gnp$ for $p=n^{-\delta}$ where $\delta>1/2$. The
main tool used to derive such a result is a careful analysis of the
distribution of edges in $\Gnd$, relying both on the switching technique and on
bounding the probability of exponentially small events in the configuration
model.
