You can't just use the regular abstract environment provided by the report document class, since it puts it on a page of its own. However, a slight modification to that environment (or creating a similar one without the conditional page breaking) - provided below as chapabstract - works without problem:

\documentclass{report}
\usepackage{changepage}% http://ctan.org/pkg/changepage
\usepackage{lipsum}% http://ctan.org/pkg/lipsum
\makeatletter
\newenvironment{chapabstract}{%
\begin{center}%
\bfseries Chapter Abstract
\end{center}}%
{\par}
\makeatother
\begin{document}
\chapter{First chapter}
\begin{chapabstract}
\lipsum[1]
\end{chapabstract}
\section{A section}
%=====
\chapter{Second chapter}
\begin{adjustwidth}{1cm}{1cm}
\lipsum[1]
\end{adjustwidth}
\section{A section}
\end{document}
changepage also provides the adjustwidth environment (where you specify the left/right indent), which allows for setting of contents in a narrower context. These two could be combined, if needed.