Start a new chapter without heading

The chapter head is typeset by \@makechapterhead, which is a macro with one argument, while the TOC entry and the heading are direct responsibiity of \@chapter and independent of \@makechapterhead. If we temporarily redefine it to simply gobble its argument, we're done.

\documentclass{report}

\makeatletter
\newcommand{\unchapter}[1]{%
  \begingroup
  \let\@makechapterhead\@gobble % make \@makechapterhead do nothing
  \chapter{#1}
  \endgroup
}
\makeatother

\pagestyle{headings}

\begin{document}
\tableofcontents

\chapter{Regular}

Text

\unchapter{No chapter head}

Text\newpage
text: check the heading

\chapter{This is regular again}

\end{document}