"My four children don't belong in a store with people carrying loaded weapons," Nicki Mcnally, spokesperson for the Indiana chapter of Moms Demand Action for Gun Sense in America said.
Moms Demand Action for Gun Sense in America is the leading the charge.
An Indiana woman started the group after the Newtown, Connecticut school shooting.
Members say they haven't seen many changes to gun laws since that terrible December day.
"We haven't gotten the success we'd like to see from our legislators in states here in Indiana and federally, so we're taking this to the corporations," McNally said.
A similar campaign last year pressured Starbucks to ban guns in its stores.
But the nation's largest supermarket chain doesn't appear to have plans to follow suit.
The company released a statement that says in part, "We don't want to put our associates in a position of having to confront a customer who is legally carrying a gun. That is why our long-standing policy on this issue is to follow state and local laws."
One long-time Kroger customer says she's torn on the issue.
"I think it's a good thing, but it's not the gun that shoots people it's a person that shoots a person. I think I'm on the fence a little bit," Deby Haymaker said.
Steve Ellis, the CEO of Top Guns in Terre Haute, is clear on his position.
"At the end of the day it's up to those corporations to allow or not allow a firearm into their store," Ellis said.
And if a business decides to not allow firearms he takes his money elsewhere.
"We boycott a few places here locally that say no firearms," Ellis said.
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