  We look at the centralizer in a semisimple algebraic group $G$ of a regular
nilpotent element, and show that its closure in the wonderful compactification
is isomorphic to the Peterson variety. It follows that the closure in the
wonderful compactification of the centralizer $G^x$ of any regular element $x$
is isomorphic to the closure of a general $G^x$-orbit in the flag variety. We
also give a description of the $G^e$-orbit structure of the Peterson variety.
