The use of they/their as an epicene pronoun for the third person singular in English is nearly a millennium old.

A good place to read up on they with singular antecedent is the Merriam-Webster's Dictionary of English Usage, free online at Google Books (link), pp.901f.

My favorite uses of the epicene they are from the Bible: e.g., So likewise shall my heauenly Father doe also vnto you, if yee from your hearts forgiue not euery one his brother their trespasses. Matt. 18:35. KJV. (See Language Log link).

Yous truly has even had a sarcastic something (link) to say about this grammatical feature of English.

Ceci n'est pas un seing.