In Chrome, the most precise cookie deletion you can perform is everything from the last hour, with no ability to select certain sites or even particular cookies. Sometimes you need a finer tool to modify or remove cookies and fortunately, Chrome's developer functionality has this kind of granularity.
To delete cookies in Chrome in a more surgical manner, point your browser at the website in question and hit Ctrl-Shift-I. A window like the one in the lead image will appear, from which you can click the "Resources" tab. In the left-hand tree view, open the "Cookies" node and you'll see a list of cookies stored for that session.
To delete a cookie, you can simply choose it in the right-hand view and press Delete. Alternatively, you can edit the contents of the cookie, a helpful feature if you're trying to diagnose a problem, or test different settings during website development. A "Clear" button is also available at the bottom of the right-hand view if you just want to nuke everything.