I found this little gem - now we like it, now we don't - at Chicago Style Q&A: Pronouns :
Question. I would swear that I saw a reference in your manual that approved of the use of “their” instead of a gender-biased singular pronoun. For example, “If the user has completed installing the program, they should put the CD-ROM back in the package,” instead of “If the user has completed installing the program, s/he should put the CD-ROM back in the package,” but on your Q&A, you dance around the answer to the question and suggest that you do NOT approve of the singular “their.” Can you tell us what is acceptable?
Answer. Yes, you saw it at 2.98 (note 9) in the fourteenth edition, but there was some regret at having written it, and we decided not to second the idea in the fifteenth edition. Though some writers are comfortable with the occasional use of they as a singular pronoun, some are not, and it is better to do the necessary work to recast a sentence or, other options having been exhausted, use he or she. For a fuller discussion of this issue, see paragraphs 5.43 and 5.202–6 in CMOS 15, including the entry for “he or she” under the “Glossary of Troublesome Expressions” at paragraph 5.202.