\chapter{Two}
\section{A section}
\lipsum \cite{Chomsky1986,Chomsky1995,Munn2005}
\subsection{A subsection}
\lipsum

\bibliographystyle{apalike}
\bibliography{MSU-thesis-testfile}
\begin{appendix}
\chapter{Tables and figures}
%  \section{A subsection} % This is a problems
\end{appendix}
% Add before bibliography call