Gilliland resigned from Sunflower, which has locations in seven states. He also founded Wild Oats Markets Inc., which was acquired by Whole Foods Market in 2007.
Gilliland was one of eight men arrested Thursday in the sting.
Sunflower said Gilliland told the company he believes he is not guilty. He could not be reached Saturday on his cell phone.
Sunflower's president and COO, Chris Sherrell, was named acting chief executive by the company's board of directors. He has been with Sunflower since it was formed in 2002.
"Sunflower appreciates the respect that Mr. Gilliland has shown for the company by his action so that his personal affairs will not affect the company," Sherrell said.
He said the change in management will not affect Sunflower's operations or its plans for expansion. The chain has 32 stores in California, Colorado, Arizona, New Mexico, Nevada, Utah and Texas.