Depends on your state.
Oregon state law has no prohibition on open carry, but allows cities and counties to regulate it if you do NOT have a CHL. Same in Missouri (they can opt out of open carry, but there's no CHL exemption, so you may face charges if you open carry on your LTC in Missouri in a city that forbids it, if the MOSC declares it constitutional).
Washington state law has no specific prohibition, but there's an "alarmed person" standard in RCW 9.41.270. Some cite examples of cases that have been cited don't apply specifically to just carrying a handgun in a holster. One case that was cited by people who were against open carrying is the State v. Spencer case. Only problem is, the guy was holding an AKM-47 and walking down the street with it. That's a LITTLE different than carrying around a handgun holstered.
I know New Mexico and Arizona allow open carry, Colorado, and Kentucky too.
Nevada does unless you're in Boulder City or North Las Vegas (grandfathered ordinance). Vermont does, Alaska does.
New Hampshire does allow open carry on foot only without a permit, and so does Alabama. Pennsylvania has the same rule, but a permit from ANY state exempts you from the prohibition against carrying a handgun in the car, and you cannot carry openly in a city of first class (Philadelphia) without a PA LTCF or other recognized permit.
Virginia has no open carry prohibition, but certain grandfathered ordinances exist, but they are not applicable to Virginia permit holders. There is legislation to completely preempt all gun laws including the grandfathered ones, but I'm not sure if it passed or where it's at now.
Florida, Texas, Oklahoma, and Illinois do not allow open carry, period, unless you're in your own home, business, etc.
Georgia allows open carry only with the firearms license for CCW. Same for Indiana, Tennessee, and Minnesota.
Rhode Island only allows open carry with a AG issued permit. The local permits (which are just as valid for CCW as AG issued permits) do not exempt from the anti-open carry laws, only the AG's permit does.
Not trying to be exhaustive, but that's the extent of my knowledge on open carry.