Chapter first (chapter name)

1.1 (section name)

1.2 (section name)

1.2.1 (subsection name)

Chapter second (chapter name)

2.1 (section name)

2.1.1 (subsection name)

2.2 (section name)

• Hi and welcome. Where are you stuck? Having the chapter unnumbered or having the sections numbered the way they are. Or producing a toc in the first place? – Johannes_B Oct 20 '14 at 7:49
• @Johannes_B: I believe, its the ordinal numbers first, second etc, as the title of the question proposes. – user31729 Oct 20 '14 at 7:50

This is a solution that depends on the book class, by removing patching the \@chapter macro, changing the \addcontentsline entry and setting it to \Ordinalstring{chapter} from fmtcount package.

\documentclass{book}

\usepackage{fmtcount}
\usepackage{etoolbox}

\makeatletter
\makeatother

\begin{document}
\tableofcontents

\chapter{Some chapter name}

\section{Number one}

\subsection{Subsec Number one}

\chapter{Another chapter name}

\section{Number one from 2nd chapter}

\subsection{Subsec Number one}

\end{document}