You wrote,
I would like the content of the fields url
and urldate
to be included in the bibliography, e.g. in the form
Available online at: https://tex.stackexchange.com, last accessed on 01.01.2020.
The chicago
bibliography style is actually quite old. For sure, it does not truly represent the bibliographic formatting guidelines of the current, viz., 17th, edition of the Chicago Manual of Style. If you need to adhere to "Chicago"'s current guidelines, you should look into using biblatex
and its biblatex-chicago
style.
If you decide to stay with BibTeX and the by now rather obsolete chicago
bibliography style, you should also be aware of the fact that it is so old that "Chicago" made no mention of how to format url
and urldate
fields back then. If a bibliography style doesn't specify what should be done with certain fields, these fields will simply be ignored by BibTeX. That's precisely what you're experiencing.
Fortunately for you, though, the chicago
bib style does specify what to do with the note
field, for virtually all entry types, including the @misc
entry type. Hence, you may want to rewrite the bib entry in question as
@misc{TestEntry.2020,
author = {Last Name, First Name},
year = {2020},
title = {Title of Homepage},
note = {Available online at: \url{https://tex.stackexchange.com},
last accessed on 01.01.2020}
}
Since this approach involves using a macro called \url
, you will also need to load a package that defines a macro by that name. I suggest you load the xurl
package, as it permits abritrary line break points in URL strings.
A full MWE (mininum working example):

\documentclass[a4paper,12pt]{article}
\begin{filecontents}[overwrite]{Literature.bib}
@misc{TestEntry.2020,
author = {Last Name, First Name},
year = {2020},
title = {Title of Homepage},
note = {Available online at: \url{https://tex.stackexchange.com},
last accessed on 01.01.2020}
}
\end{filecontents}
\usepackage{natbib}
\bibliographystyle{chicago}
\usepackage{xurl} % for "\url" macro
\usepackage[colorlinks,allcolors=blue]{hyperref} % optional
\begin{document}
\noindent
\citealt{TestEntry.2020}.
\bibliography{Literature}
\end{document}
Addendum to address the OP's follow-up request raised in a comment. To process the bibliography and citation call-outs using the biblatex
package -- more precisely: the biblatex-chicago
package -- I suggest you make some modifications to the entry at hand:
The good news is that biblatex
does know about fields called url
and urldate
. However, it's necessary to cast the contents of the urldate
field in yyyy-mm--dd
format (aka ISO8601 format): 2020-01-01
is good, but 01.01.2020
is not.
I would change the entry type from BibTeX's catch-all @misc
to @online
.
Unless you have a very good reason for using BibTeX rather than biber
as the back-end program need to sort the bibliographic entries, do run biber
, not BibTeX.

\documentclass[a4paper,12pt]{article}
\begin{filecontents}[overwrite]{Literature.bib}
@online{TestEntry.2020,
author = {Last Name, First Name},
year = {2020},
title = {Title of Homepage},
url = {https://tex.stackexchange.com},
urldate= {2020-01-01}
}
\end{filecontents}
\usepackage[backend=biber]{biblatex-chicago}
\addbibresource{Literature.bib}
\usepackage{xurl} % for "\url" macro
\usepackage[colorlinks,allcolors=blue]{hyperref} % optional
\begin{document}
\noindent
\citeauthor{TestEntry.2020}, \citeyear{TestEntry.2020}
\printbibliography
\end{document}