How can I create a blurred Chapter title such as this?

How can I create a blurred Chapter title such as this?

One possibility; the idea is to use several copies of the string with different opacity and offsets (basically, a modification of the idea used in the answer to Blur the text so it's not readable).
First, a TikZ-free solution with the text and four offset copies:
\documentclass{book}
\usepackage{xcolor}
\usepackage{titlesec}
\usepackage{lmodern}
\titleformat{\chapter}[display]
{\normalfont\fontsize{37}{48}\sffamily\filleft}
{{\color{gray!15}\chaptertitlename~\thechapter}\hspace*{3.5pt}%
\llap{\color{gray!15}\chaptertitlename~\thechapter}\hspace*{-1.75pt}%
\llap{\color{gray!15}%
\raisebox{1.75pt}[0pt][0pt]{\chaptertitlename~\thechapter}}%
\llap{\color{gray!15}%
\raisebox{-1.75pt}[0pt][0pt]{\chaptertitlename~\thechapter}}%
\llap{\color{gray!40}%
\chaptertitlename~\thechapter}}
{20pt}{\huge\color{blue!50!black}}
\begin{document}
\chapter{A Test Chapter Title}
\end{document}

And a solution using TikZ with the text and eight offset copies:
\documentclass{book}
\usepackage{xcolor}
\usepackage{tikz}
\usepackage{titlesec}
\usepackage{lmodern}
\titleformat{\chapter}[display]
{\normalfont\fontsize{37}{48}\sffamily\filleft}
{\begin{tikzpicture}[
baseline,
every node/.style={anchor=base,inner sep=0pt,outer sep=0pt,align=right},
transparency group]
\foreach \c in {0,...,7}
\node[shift={(45*\c:1.65pt)},opacity=0.03] {\chaptertitlename~\thechapter};
\node[opacity=0.13] {\chaptertitlename~\thechapter};
\end{tikzpicture}%
}
{20pt}{\huge\color{blue!50!black}}
\begin{document}
\chapter{A Test Chapter Title}
\end{document}

The \foreach loop (thanks to Tom Bombadil for this suggestion) allows to easily control the number and placement of offset copies.
I used the titlesec package interface, but this can be done directly, without using packages, by redefining the \@makechapterhead command (in report or book), or the command in charge of typeseting the chapter headings in any other document class.
foreach loop for that: \foreach \c in {0,...,3} together with \node[shift={(90*\c:1.5pt)}]. This would make it easier to modify the number of copys and distances.
– Tom Bombadil
Jun 10 '13 at 00:37
external library, set the next file name to something dependent of the chapter counter so that even if one changes the order of chapters the process is only done once for every integer (unless you change fonts or the actual process).
– Qrrbrbirlbel
Jun 10 '13 at 00:50