Are you talking about when the .tex file was opened (for editing), or when a particular .tex file was last compiled. If the later then I might have some answers:
Opened? Not that I know of. Compiled? Yes. I do this all the time. Check out the currfile and datemod packages. For example I use the following to put the 'last time compiled' stamp in the footer of the first page (which I specify as 'plain') of each chapter of one of my books:
\usepackage{currfile}
\usepackage{filemod}
\usepackage{fancyhdr}
\renewcommand*{\thefilemoddate}[3]{#2.#3.#1}
\fancypagestyle{plain}{%
%\fancyhf{} % clear all header and footer fields
\fancyhead[R]{}
\fancyhead[L]{}
\fancyfoot[R]{\footnotesize{\sffamily\filemodprintdate{\currfilepath}}}
%\fancyfoot[R]{\footnotesize\sffamily{c. \mdyydate\today}} % compile date - lower right
\fancyfoot[L]{\footnotesize\sffamily{\copyright~my name (2013)}}