Update (March 2021)
In version 2.1 (2021-03-27), biblatex-chicago introduced the dashed option which can be set to false to print repeated names in the bibliography (just like in biblatex's standard authoryear style).
\documentclass[british]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{babel}
\usepackage{csquotes}
\usepackage[authordate, backend=biber, dashed=false]{biblatex-chicago}
\addbibresource{biblatex-examples.bib}
\begin{document}
\autocite{knuth:ct:a,knuth:ct:b}
\printbibliography
\end{document}
The documentation now explains (for v2.3a on p. 73 in §4.4.2 Pre-Set chicago Options):
Constanza Cordoni has requested a way to turn off the 3-em dash for replacing repeated names in the bibliography, and the Manual admits that some publishers prefer this, as the
dash can carry with it certain inconveniences, especially for electronic formats (14.67). Some of biblatex’s standard styles have a dashed option, so for compatibility purposes I’ve provided the same. By default I have set it to print the name dash, but you can set
dashed=false globally, per type, or per entry to repeat names as and when required.
Solution for older releases
In the standard styles you could turn off the dash with the option dashed=false, see Get full name twice in Bibliography.
The styles of biblatex-chicago do not know that option and do not allow you to turn the dash off easily. It is a feature of the Chicago Manual of Style bibliography styles that they replace subsequent mentions of the same author list with a dash.
Since there is no option to turn off the dash, there is no convenient way to get rid of it, you need to play with internal macros. You can essentially tell biblatex to forget who the last author was by undefining \bbx@lasthash, which forces the style to never use the dash to replace the name.
\documentclass[british]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{babel}
\usepackage{csquotes}
\usepackage[authordate,backend=biber]{biblatex-chicago}
\addbibresource{biblatex-examples.bib}
\makeatletter
\AtEveryBibitem{\global\undef\bbx@lasthash}
\makeatother
\begin{document}
\cite{knuth:ct:a,knuth:ct:b}
\printbibliography
\end{document}

Please note that the styles of biblatex-chicago should ideally be loaded using the wrapper package biblatex-chicago and not the normal biblatex package (as shown in the MWE). But then you can't use the natbib option.
dashed=falseto yourbiblatexloading options. – moewe Oct 17 '18 at 10:09biblatexoptions. You should have\usepackage[...]{biblatex}somewhere. Adddashed=falseto the...in square brackets in that line. – moewe Oct 17 '18 at 10:18\usepackage[style=chicago-authordate,natbib=true,backend=biber,dashed=false]{biblatex}Unfortunately I get the following error with it
– Leon Oct 17 '18 at 10:26/usr/local/texlive/2017/texmf-dist/tex/latex/biblatex/biblatex.sty, line 13053 Package keyval Error: dashed undefined. See the keyval package documentation for explanation. Type H <return> for immediate help. ... l.13053 \blx@processoptions Try typing <return> to proceed. If that doesn't work, type X <return> to quit.chicago-authordatedoes not have such an option. The CMS wants that dash. – moewe Oct 17 '18 at 10:36