You can redefine \chapter using xparse, a bit like in this answer of egreg. Note that I only do the redefinition after \tableofcontents has been used, otherwise you would see “Contents” twice in a row, since the \tableofcontents is introduced as a \chapter* (\tableofcontents would add its own title to the table of contents).
\documentclass{report}
\usepackage[a5paper,landscape]{geometry} % small page size for the screenshot
\usepackage{titlesec,titletoc,xparse}
\usepackage{lipsum}
\titleformat{name=\chapter}[display]
{\normalfont\huge}
{\chaptername\ \thechapter}
{1ex}
{}
\titleformat{name=\chapter,numberless}[display]
{\normalfont\huge}
{}
{0pt}
{}
\let\latexchapter\chapter
\newcommand*{\redefineChapter}{%
\RenewDocumentCommand{\chapter}{ s O{##3} m }{%
\IfBooleanTF{##1}
{\latexchapter*{##3}%
\addcontentsline{toc}{chapter}{##2}}
{\latexchapter[##2]{##3}}%
}%
}
\begin{document}
\tableofcontents
\redefineChapter
\chapter*{An unnumbered chapter}
\lipsum[1]
\chapter{A numbered chapter}
\lipsum[1]
\end{document}

With this code, you can even use \chapter* with an optional argument in order to specify a special variant of the title for the table of contents:
\chapter*[Title in the toc]{An unnumbered chapter}
