There's 9 states that I know of that do not require a person to have a permit to carry a handgun either concealed or opening but you must abide by all local, state and even Federal laws when carrying the gun without a permit and you must be legally able to have a firearm in your possession and it must also be registered legally in your name.
The states of West Virginia,Vermont, New Hampshire, Missouri, Mississippi,Kansas, Maine, Alaska and Arizona don't require a permit to carry a firearm opening or concealed.