Following minimal document:
\documentclass{report}
\begin{document}
\renewcommand*\thechapter{\Roman{chapter}}
\tableofcontents
\setcounter{chapter}{6} % Problem starts at chapter 7
\chapter{Seven}
\chapter{Eight}
\section{Eight-one}
\section{Eight-two}
\end{document}
yields this output (cut to size for your convenience):

Clearly, the chapter (and section) headings hang into the chapter (section) numbers. For the previous chapter numbers, this isn’t a problem since all chapter titles are aligned to the same column and the numbers I–VI are sufficiently narrow.
(The same happens regardless of document type, I’m actually using scrreprt with the same result.)
How can I prevent this?

scrreprtmay be easier. A solution forreportdoesn't necessarily have to be the best for scrreprt. – Stefan Kottwitz♦ Dec 19 '10 at 17:38screprt. I didn’t find a solution in the KOMA documentation, though. – Konrad Rudolph Dec 19 '10 at 18:02