Some are vowing to boycott the company, while others applaud the support of traditional marriage.
Chattanooga resident Whit Gardner said via Twitter she always avoids Chick-fil-A because of leaders' views.
Another local resident, Britton Stansell, said he will be eating more Chick-fil-A because company leaders are "operating with standards they believe in, when most companies would fold."
Last week, Chick-fil-A President Dan Cathy said the company was "guilty as charged" in its opposition to same-sex marriage.
This prompted Boston Mayor Thomas Menino to express displeasure with the stance. He promised to make it "very difficult" for the company to get the needed business licenses to open in Boston, according to the Christian Science Monitor.
Former presidential candidate and former Arkansas Gov. Mike Huckabee has called for a Chick-fil-A Appreciation Day.
Local resident Jason Wright said via Facebook he doesn't understand why people are surprised by Cathy's comments.
Company leaders don't make their Christian values a secret, he said, using the example that the company is closed on Sundays.
"They have always held fast to their Christian beliefs and have been quite public about it," he said. "I always want a [chicken] biscuit on Sunday morning, then think, 'Crap, they aren't open on Sundays!'"
Another area resident pointed to this graphic as evidence that Chick-fil-A's business will not be harmed by the president's comments.
Local Chick-fil-A spokeswoman Linda Lim said she hasn't heard any local feedback about the situation yet, but she said she would check with area managers to see if they have heard any comments.