Several American states allow people to carry licensed guns in plain view despite the country's epidemic of school and mass shootings.
Starbucks has been thrust into the bitter national debate on tougher gun control laws because it defers to local legislation on carrying guns openly.
That has led opponents of stricter gun laws to stage so-called Starbucks Appreciation Days at some of its cafes.
In a statement issued yesterday night, Starbucks chairman and CEO Howard Schultz said the coffee chain known around the world "does not want these events in our stores."
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Schultz said Starbucks had found itself unwillingly in the middle of the national debate.
"That's why I am writing today with a respectful request that customers no longer bring firearms into our stores or outdoor seating areas," Schultz wrote.
This applies even in states where so-called open carry laws -- legislation that lets people bear a gun openly in public -- are in force, he said.
He insisted the directive was a request and not an outright ban.
That's for several reasons: the company wants to give "responsible gun owners" a chance to honor the request, and because a ban might force employers to confront customers with guns.
"The presence of a weapon in our stores is unsettling and upsetting for many of our customers," he wrote.