Basically you will want to renew the command that deals with the chapter title formatting. This link explains it pretty well. Since you don't want the starred version, you can settle with changing the normal version.
\renewcommand{\@makechapterhead}[1]{%
\vspace*{50\p@}%
{\parindent \z@ \raggedright \normalfont
\hrule % horizontal line
\vspace{5pt}% % add vertical space
\ifnum \c@secnumdepth >\m@ne
\huge\scshape \@chapapp\space \thechapter % Chapter number
\par\nobreak
\vskip 20\p@
\fi
\interlinepenalty\@M
\Huge \scshape #1\par % chapter title
\vspace{5pt}% % add vertical space
\hrule % horizontal rule
\nobreak
\vskip 40\p@
}%
}
What you will want to do is comment out the line that has the Chapter number
comment and the surrounding comments (everything inside of the if) to get rid of the extra space. You can customize this command a little further if you want to change the looks of the chapter headings. Take note that you have to wrap this in \makeatletter
and \makeatother
to change the catcode for the @ symbol. So you would get:
\makeatletter
\renewcommand{\@makechapterhead}[1]{%
\vspace*{50\p@}%
{\parindent \z@ \raggedright \normalfont
\hrule % horizontal line
\vspace{5pt}% % add vertical space
\interlinepenalty\@M
\Huge \scshape #1\par % chapter title
\vspace{5pt}% % add vertical space
\hrule % horizontal rule
\nobreak
\vskip 40\p@
}%
}
\makeatother
And a simple test document
\documentclass{report}
\begin{document}
\makeatletter
\renewcommand{\@makechapterhead}[1]{%
\vspace*{50\p@}%
{\parindent \z@ \raggedright \normalfont
\hrule % horizontal line
\vspace{5pt}% % add vertical space
\interlinepenalty\@M
\Huge \scshape #1\par % chapter title
\vspace{5pt}% % add vertical space
\hrule % horizontal rule
\nobreak
\vskip 40\p@
}%
}
\makeatother
\tableofcontents
\chapter{Test}
some test text
\end{document}
Would look like this:

edit: too slow :(