I'm writing an essay in CMS style. I have a quotation I use in the beginning of the essay that I cite. I reference part of the quote later in quotation marks. Do I need a citation the second time?
If you cite an included full quotation and immediately discuss it phrase by phrase, then you don't have to cite every phrase, every time. That's just silly. I'd go so far as to say it's insulting, as it implies you think your readers are morons.
But if the partial quotes are some paragraphs removed from the original quote, with discussion between that might reasonably cause a reader to forget the original citation, then definitely you should re-cite (but using only author and page number for the re-cites, as @Sel pointed out).
Caveat: If you cite another work by the same author in between the original cite and the re-cite, then your first re-cite of the original quote must include enough info to make clear which work by that author you are referring to. Check the guidelines for particulars, but use good judgment. For example, if you are discussing different publishers' versions of "The Hobbit," then you might need a full citation every time you switch the version you're referring to. But if the different versions came out in different years, then re-cites could just use the publication date to differentiate.