\documentclass{book}

%% Exercises

\let\counterwithout\relax
\let\counterwithin\relax
\usepackage{chngcntr}

\usepackage{exercise}
\counterwithin{Exercise}{chapter}

\renewcommand{\ExerciseHeader}{
\noindent\textbf{\ExerciseName~\ExerciseHeaderNB~\ExerciseHeaderTitle~\ExerciseHeaderOrigin}
}

\begin{document}

\chapter{Chapter Title Here}

\section{Section Title Here}

\begin{Exercise}
\begin{itemize}
\item Item 1
\item Item 2
\end{itemize}
\end{Exercise}

\begin{Exercise}
\begin{itemize}
\item Item 1
\item Item 2
\end{itemize}
\end{Exercise}

\end{document}