They aren't going after him, just probably opposing the registration in front of the PTO.
If you are a party who may be damaged by issuance, you can challenge the registration before it issues.
EDIT: Actually, looking closer they aren't even opposing, the PTO issued the rejection directly, without any involvment from chick-fil-a at all. It never even made it to the opposition stage.
http://tsdr.uspto.gov/#caseNumber=85412053&caseType=SERI...
There are no filings or documents from chick-fil-a in here at all. The examiner apparently came up with the rejection reason on their own (any communications chick-fil-a had by phone with the examiner would have been on record and here as well)
It's even been through two examiners now.
That said, the current examiner's arguments seem like complete and total BS.
Double edit: I take it back, it looks like one of these actually is a notice of a letter of protest (december 22nd, 2011), which functions much like an opposition. However, only the outgoing notice that a letter of protest is filed is there, the actual letter of protest (received, december 2011), presumably from chick-fil-a, is for some reason, not in the documents.
Sorry, i'm much more used to reading patent dockets than trademark ones :)