They did so in a letter, stating that they simply follow or allow what local and state law allows. I really do believe that concealed carry is the way to go. Not everyone agrees with me, and for them:

So far, Kroger seems to being doing right by its customers. They have yet to cave to Bloomy’s intimidation tactics. Kroger has done exactly what a non-partisan business should do: They told a bunch of activist liberals that if guns are that big of a problem, the appropriate action should be taken with the city council, state legislature, or federal lawmakers. Not their local purveyor of milk and produce.

The key there is, “so far,” since we’ve seen other large chains cave after a time.