Griffin's husband, Robert, told WFMY the young employees let the couple in after closing, and were quick to help under pressure.
"I hear high pitched screaming and I was like, OK-- this is serious. This is happening," said Brenda Enriquez, the Chick-fil-A employee who called 911.
In a Facebook post, Robert Griffin said management brought them clean towels as Falon Griffin started to go into labor in the restaurant's bathroom stall.
She gave birth to a girl, Gracelyn Griffin, about 15 minutes before paramedics arrived.
"Her birth certificate reads 'Born in Chick-fil-A' and the hospital had me sign the birth certificate as attending physician," Robert Griffin wrote on Facebook.
Griffin said that Chick-fil-A has offered baby Gracelyn free Chick-fil-A for life and a guaranteed first job.