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
\patchcmd{\@chapter}{\addcontentsline{toc}{chapter}{\protect\numberline{\thechapter}#1}}{\addcontentsline{toc}{chapter}{\protect{\numberline{\chaptername~\Ordinalstring{chapter} #1}}}}{}{}
\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}

toc
in the first place?first
,second
etc, as the title of the question proposes.