Chapter headings are set, by default, using \raggedright. However, this does not avoid hyphenation necessarily. Yet one can patch the respective chapter heading macros to avoid hyphenation via \hyphenpenalty=10000:

\documentclass{report}%
\usepackage{etoolbox}% http://ctan.org/pkg/etoolbox
% http://mentalfloss.com/article/50611/12-exceptionally-long-or-extremely-special-words
\hyphenation{sub-der-ma-to-gly-phic}
\setlength{\textwidth}{.5\textwidth}% Just for this example
\begin{document}
\chapter{This subdermatoglyphic title is long}
\makeatletter
% \patchcmd{<cmd>}{<search>}{<replace>}{<success>}{<failure>}
\patchcmd{\@makechapterhead}{#1}{\hyphenpenalty=10000 #1}{}{}% Patch \chapter
\patchcmd{\@makeschapterhead}{#1}{\hyphenpenalty=10000 #1}{}{}% Patch \chapter*
\makeatother
\chapter{This subdermatoglyphic title is long}
\end{document}
Note that avoiding hyphenation could cause "Overfull \hbox" warnings, which is exactly the case above. Perhaps it's an extreme case, but still.
\chapter{\mbox{maybe} \mbox{this} \mbox{would} \mbox{work}?}– gerrit Nov 21 '11 at 22:19