Rearrange references in the bibliography

I suggest you use the noopsort trick that works with both bibtex and biber. The macro is defined as

providecommandnoopsort[1]{}

This seems like a trivial command, which takes one argument and outputs nothing via LaTeX. But it's not useless, as it can be used to influence how bibtex and biber sort entries. In the code below, observe the noopsort{a} and noopsort{b} instructions at the start of the entries' respective title fields. Since the biblatex-chicago style sorts entries by the author, year, and title fields, the noopsort directives let you achieve your formatting goal.

The noopsort trick is very versatile and has many possible uses. See, for instance, Put Chinese-language entries before English-language entries in the bibliography for an example of how to use noopsort to place, you guessed it, all Chinese-language entries before the other entries in the bibliography.

documentclass{article}
%%usepackage[utf8]{inputenc} % that's the default nowadays
providecommandnoopsort[1]{}

begin{filecontents}[overwrite]{bib.bib}
@article{Williamson.1968a,
 author = {Williamson, Oliver E.},
 year = {1968},
 title = {noopsort{a}Economies as an Antitrust Defense: The Welfare Tradeoffs},
}
@article{Williamson.1968b,
 author = {Williamson, Oliver E.},
 year = {1968},
 title = {noopsort{b}Economies as an Antitrust Defense: Correction and Reply},
}
end{filecontents}

usepackage[authordate,strict,backend=biber,bibencoding=inputenc]{biblatex-chicago} 
addbibresource{bib.bib}

begin{document}
This is the first citation parencite{Williamson.1968a}.
In the same year, a correction was published parencite{Williamson.1968b}.

printbibliography
end{document}