Chik-fil-A's president, Dan Cathy, has spoken out against gay marriage on several occasions, most recently in a tweet after the Supreme Court ruled the Defense of Marriage Act (DOMA) unconstitutional. Cathy wrote that it was a "sad day for our nation." The tweet was taken down and Chik-fil-A issued a statement on its website saying:
"Dan recognizes his views do not necessarily represent the views of all Chick-fil-A customers, restaurant owners and employees, so he removed the tweet to eliminate any confusion."
Chik-fil-A has also reported that the company has stopped charitable giving to some of the more controversial anti-gay groups, though much of its giving still goes to Christian groups, most of which support a traditional view of marriage that excludes gays.
So, one could conclude that Chik-fil-A is certainly not supporting gay marriage, though the company has not come out against it either, while the personal views of the president are against gay marriage. It's important to separate one person's views from an entire company's stance, but also to realize that the two may be connected.