The default \chapter command issues three different spaces to set the chapter heading:
Space from the top of the text block to the word Chapter; default is 50pt.
Space between Chapter and the chapter title; default is 20pt.
Space between the chapter title and the chapter body text; default is 40pt.
All of this is made by the macro \@makechapterhead (from book.cls; emphasis added):
\def\@makechapterhead#1{%
\vspace*{50\p@}% <------------------------------------ (1)
{\parindent \z@ \raggedright \normalfont
\ifnum \c@secnumdepth >\m@ne
\if@mainmatter
\huge\bfseries \@chapapp\space \thechapter
\par\nobreak
\vskip 20\p@% <--------------------------------- (2)
\fi
\fi
\interlinepenalty\@M
\Huge \bfseries #1\par\nobreak
\vskip 40\p@% <------------------------------------- (3)
}}
For unnumbered chapters, there are still two spaces (1) and (3) above given as part of \@makeschapterhead:
\def\@makeschapterhead#1{%
\vspace*{50\p@}% <------------------------------------ (1)
{\parindent \z@ \raggedright
\normalfont
\interlinepenalty\@M
\Huge \bfseries #1\par\nobreak
\vskip 40\p@% <------------------------------------- (3)
}}
You can either get rid of these using an etoolbox patch, but it may be better to just write your own \@makechapterhead macro:

\documentclass{book}
\makeatletter
\renewcommand{\@makechapterhead}[1]{%
{\noindent\raggedright\normalfont% Alignment and font reset
\huge\bfseries \@chapapp\space\thechapter~~#1\par\nobreak}% Formatting
\vspace{\baselineskip}% ...just a little space
}
\makeatother
\usepackage{showframe}% Just to show the frame
\begin{document}
\chapter{Example}
How do I get chapter to go higher on the page. In order to get as many words per page.
\end{document}
You can do something similar for \@makeschapterhead.
\chapterthen? Why not use something like a\section? – Werner May 16 '16 at 17:12showframeto show the text margins. – Steven B. Segletes May 16 '16 at 17:15