In a post on their Facebook page, the Jim Henson Company said that CEO Lisa Henson had always supported gay rights.
"The Jim Henson Company has celebrated and embraced diversity and inclusiveness for over fifty years and we have notified Chick-Fil-A that we do not wish to partner with them on any future endeavors," the statement said.
The company also said they would donate funds received from Chick-fil-A to gay rights organization GLAAD.
Chick-fil-A has long been known for its commitment to conservative Christian values (they're never open on Sundays) but President and CEO Dan Cathy affirmed the company's position on gay marriage in an interview with the Baptist Press earlier this month.
"We are very much supportive of the family -- the biblical definition of the family unit. We are a family-owned business, a family-led business, and we are married to our first wives. We give God thanks for that," Cathy said.
Gay rights supporters are encouraging boycotts of the fast food chain--Ed Helms of "The Office" tweeted that Chick-fil-A had "lost a loyal fan."
"Chick-Fil-A doesn't like gay people? So lame. Hate to think what they do to the gay chickens!" Helms said.
Dustin Lance Black, who wrote "J. Edgar" and "Milk," tweeted, "'Guilty as charged!' Chick fil A sauce = $ for bigotry. Just say no, Los Angeles!"
Republican politician Mike Huckabee, however, launched a Facebook event called "Chick-fil-A Appreciation Day," slated for August 1, hoping to counter what he called "vicious hate speech and intolerant bigotry from the left."
In response, there's now a "National Same Sex Kiss Day," encouraging same-sex couples to kiss in front of Chick-fil-A's around the country on August 3.