According to the US Postal Inspection Service, these chain letters are illegal: they're requesting money or other items of value, and promising a substantial return to the participants -- a return that's highly unlikely in the first place.
The "secret sister" scam is nothing new. Similar scams have made the rounds on Facebook in past few years, including book exchanges.
Mathematicians - and the postal service alike - say there's no way everyone can come out with 36 gifts or books.
Not only are these posts pyramid schemes, meaning those at the bottom of the chain likely get no gifts at all, but they're against federal law.