There's the law. Looks like it's illegal on private property if posted. Section O (4 5ths of the way down the page). states:
O. The granting of a concealed handgun permit shall not thereby authorize the possession of any handgun or other weapon on property or in places where such possession is otherwise prohibited by law or is prohibited by the owner of private property.
PS. Love your signature! I'd love to have that store down the street.