From what I've read about the company in operating on its Christian values, "sinfulness" is a disqualifier for those who might like to acquire a Chik-fil-a franchise. No evidence it's come into play, but that would seem possible grounds to disqualify homosexuals as franchise holders.
http://www.forbes.com/forbes/2007/0723/080.html
http://nexus.som.yale.edu/chick-fil-a/ (Yale case study)

In addition to the NH franchisee, the only one in Chicago has spoken out in support of LGBT rights. Some gay employees have been having a hard time of it lately: Huff Post.

Corporate monies (through the WinShape Foundation - their charitable arm) have gone to organizations that actively work against the legalization of same-sex marriage, and some of those organizations also are seen to have an agenda hateful toward homosexuals. Detailed here: http://equalitymatters.org/factcheck/201207020001

Here's an even-handed statement from a Christian perspective: Rachel Held Evans: Some words for Christians on both sides of the Chick-fil-A war (written before the C-F-A Appreciation Day). She has a sad post today: When you feel out of step with your religious community....

I think the Boston & Chicago mayors are making a big mistake, and I note that there are prominent statements from activists for marriage equality making statements to that effect (Andrew Sullivan, and Steve Salbu, in an NY Times op-ed).

~ Becky in Tucson