Restaurant chains: We're not pulling a Chipotle

Despite Chipotle's request that customers refrain from bringing guns into its locations, many restaurant chains plan to look to state legislatures rather than internally when deciding how to approach the touchy gun debate.

"Dunkin' Donuts and Baskin-Robbins restaurants are owned and operated by individual franchisees who are required to follow all federal, state and local laws with regard to firearms," said a Dunkin' Brands spokeswoman in a statement.

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Each state allows people to carry concealed handguns with varying restrictions and permit requirements, said Robert Spitzer, a political science professor at SUNY Courtland and author of five books on gun policy.

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Rich Jeffers, director of communications at Darden Restaurants, the parent company of Olive Garden, Red Lobster and LongHorn Steakhouse, said by email, "Our approach has always been that we abide by all local and state laws."

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McDonald's spokeswoman Lisa McComb said the company's policy remains the same even after Chipotle issued its new policy. Chipotle's followed a similar request from coffee chain Starbucks for customers not to bring firearms into its locations.

"While we respect the differing views of all our customers, McDonald's company-owned restaurants follow local, state and federal laws as it relates to open carry weapons in our restaurants. For franchisee-owned restaurants, operational decisions regarding open carry weapon laws are made by the independent franchisee," the company policy states.

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Still, the fast-food giant expects franchisees to follow state, local and federal laws.

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Chicken chain Zaxby's said it looks to local law and to its licensees to make the decision about what's best for their individual markets.

But following the Chipotle decision, Zaxby's is a taking a second look at its policy.

"Obviously, this is an issue that is becoming increasingly contentious, and as we continue to grow our number of restaurant locations and geographical footprint, it's something that we must examine further in order to determine how best to move forward," a representative said.

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While neither Chipotle nor Starbucks has banned firearms outright, it's within their legal right as a business, Spitzer said.

"I cannot think of a state offhand that does not give a private establishment some ability to control gun carrying within it," Spitzer said. "Generally speaking private businesses have a recognized ability to say that customers or employees cannot carry guns in if they make that policy known."

As gun right activists tote firearms openly to establishments to make a statement, Spitzer said he's seen more private businesses ask customers to leave guns at the door.

"That's been met in part with more resistance because average people tend to recoil when they see someone walking around with a gun," he said.

"Companies are not interested in controversy," Spitzer added.

A variety of chains including TGI Fridays, Subway and Cheesecake Factory declined to comment to CNBC about their gun policies.

—By CNBC's Katie Little