\documentclass{book}

\input TeX4ht.sty
\Preamble{html}   \begin{document}
\EndPreamble

\TocAt{section,subsection,/likechapter}
\CutAt{subsection,section,likechapter}

\section{My heart} is not
haughty,
\subsection{nor mine} eyes lofty:

\section{neither do}  I exercise
myself in great matters,
\subsection{or in} things
\subsection{too  high} for me.

\chapter*{Psalms}

\section*{(131:1)}

\end{document}