Change "chapter" to "Chapter" - How to do this using autoref?

The manual of the hyperref package explains how to achive this on page 17.

Edit: This answer assumes that you actually want to use the babel package. If this is not the case, just redefine \chapterautorefname at the \begin{document} hook: see Bernard’s answer for instructions on how to do this.

\documentclass{book}

% \usepackage{siunitx}
% \usepackage{nomencl}
% \usepackage{amsmath}
% \usepackage{nicefrac}
% \usepackage{nomencl}
% \usepackage{amsmath}
% \usepackage{amsthm}     
% \usepackage{amssymb}
\usepackage[english]{babel}
\usepackage{hyperref}
\addto\extrasenglish{%
  \def\chapterautorefname{Chapter}%
}
\begin{document}
       \chapter{Before We Begin}
       In \autoref{Chapter2}, we will talk about how to live a full life.
       \chapter{Begin}
       \label{Chapter2}
       Live until you die\textellipsis~:-)
\end{document}

Here’s the output I get:

Addition

Of course, the same mechanism works for other titles as well:

\documentclass{book}

\usepackage[english]{babel}
\usepackage{hyperref}
\addto\extrasenglish{%
  \def\chapterautorefname{Chapter}%
  \def\sectionautorefname{Section}%
  \def\subsectionautorefname{Subsection}%
  \def\subsubsectionautorefname{Subsubsection}%
  \def\paragraphautorefname{Paragraph}%
  \def\subparagraphautorefname{Subparagraph}%
}
\begin{document}
       \chapter{Before We Begin}
       In \autoref{Chapter2}, we will talk about how to live a full life.
       \chapter{Begin}
       \label{Chapter2}
       Live until you die\textellipsis~:-)
\end{document}

For a complete list of the available names, see the file hyperref.sty at lines, say, 3220–3235.

Whether you use babel or not, this works (no problem if you only use the English language – otherwise @Gustavo Mezzeti's answer is more appropriate):

\documentclass[english]{book}

\usepackage{siunitx}
\usepackage{nomencl}
\usepackage{amsmath}
\usepackage{nicefrac}
\usepackage{amsthm}
\usepackage{amssymb}
%
\usepackage{babel}
\usepackage{hyperref}
\AtBeginDocument{\def\chapterautorefname{Chapter}}%

\begin{document}

       \chapter{Before We Begin}
       In \autoref{Chapter2}, we will talk about how to live a full life.
       \chapter{Begin}
       \label{Chapter2}

\end{document}