When I’m editing footnotes or bibliographies, I often see authors including access dates for all online sources, even those that are unlikely to change over time (such as an article in an online scholarly journal or a major newspaper). The Chicago Manual (14.12) is here to free you from this burden!
An access date—that is, the self-reported date on which an author consulted a source—is of limited value: previous versions will often be unavailable to readers; authors typically consult a source any number of times over the course of days or months; and the accuracy of such dates, once recorded, cannot readily be verified by editors or publishers. Chicago does not therefore require access dates in its published citations of electronic sources unless no date of publication or revision can be determined from the source.Chicago Manual of Style, 17th ed., 14.12, “Access dates”
The same section does note that some publishers (or professors, in the case of student work) do require access dates, so it’s worth keeping track of them in case you end up needing them. But in most cases, at least in the humanities, you can reserve access dates for cases where no date of publication can be found, or where the content at the link is not stable.
When you do use access dates, they should follow the format shown in CMOS 14.176 and 14.207—right before the URL, set off by commas in footnotes and periods in bibliography entries (not parentheses!).