\makeatletter
\renewenvironment{theindex}
 {\pagestyle{plain}\parindent\z@
  \parskip\z@ \@plus .3\p@\relax
  \let\item\@idxitem}
 {\thispagestyle{plain}}
\makeatother
\begin{multicols}{3}[\chapter*{Index}\addcontentsline{toc}{chapter}{Index}]
  \printindex
\end{multicols}