\documentclass[twocolumn,a4paper,10pt]{book}
\usepackage[explicit]{titlesec}
\usepackage{lipsum}% just to generate some text
\newcommand\chapquote[2]{%
\titleformat{\chapter}[display]
{\normalfont\Huge\bfseries\filcenter}{\chaptertitlename\ \thechapter\vskip10pt#1}{0pt}
{\normalsize\parbox[t]{10cm}{\normalfont\itshape#2}}}
\titleformat{\chapter}[display]
{\normalfont\Huge\bfseries\filcenter}{\chaptertitlename\ \thechapter\vskip10pt#1}{0pt}
{\Huge}
\begin{document}
% a chapter with quotation
{\chapquote{Test chapter one}{\lipsum[1]}
\chapter{Test chapter one}}
\lipsum[1-2]
% a chapter without quotation
\chapter{Test chapter two}
\lipsum[1-3]
\end{document}