  The Shi arrangement ${\mathcal S}_n$ is the arrangement of affine hyperplanes
in ${\mathbb R}^n$ of the form $x_i - x_j = 0$ or $1$, for $1 \leq i < j \leq
n$. It dissects ${\mathbb R}^n$ into $(n+1)^{n-1}$ regions, as was first proved
by Shi. We give a simple bijective proof of this result. Our bijection
generalizes easily to any subarrangement of ${\mathcal S}_n$ containing the
hyperplanes $x_i - x_j = 0$ and to the extended Shi arrangements.
