Some are calling a Publix manager a hero for chasing after a suspect who held up the store on US-41 and College Parkway in Lee County. However, Publix officials aren't exactly happy.

Around 6 p.m. Tuesday night, a man walked into the Publix store and handed the clerk a note demanding cash. The robber then threatened to shoot employees and hurt customers. When he walked outside, the store's manager, Jason Edouard, chased after him.

Edouard and the suspect ran across the parking lot, crossed over busy US-41 and fought in a parking lot across the street. Edouard tried to keep the suspect from getting into a car, but the man got away.

"I think it's commendable and heroic," said shopper Carol Lassen. "People have to take a stand, times are tough for everybody."

But Publix officials say Edouard's actions are not in line with company policy.

"We want our associates to remain calm and not resist, argue or touch the robber," said Publix spokesperson Shannon Patten. "No amount of money is worth more than the lives of our associates and customers."

The company won't say if the store manager will be demoted or punished for breaking company policy. However, the supermarket chain says he won't be fired.

Deputies have security camera video and a good description of the suspect. The Lee County Sheriff's Office says it hopes to make an arrest soon.