I've always disagreed with listing "private property" in the list of prohibited places.
My understanding of §18.2-308.O is that it was placed there solely to clarify that holding a CHP does not over-ride the rights of a property owner to restrict you from carrying. That is what it says, in fact*. On this pamphlet, it's included in a long list of places where the act of carrying is a violation of the law. That is not the case in Virginia, where the only consequence of carrying against the wishes of the owner is if you choose to not leave, and then it's trespassing. This is particularly a problem in an informational pamphlet because some other states do attach a criminal element to carrying on private property when prohibited.
If it stays on the list, at the least we should add some indication that "trespass" is the consequence, not a gun-related criminal charge.
*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.