"License holders are among the most honest in the states," said Joe Eaton of Warren County. "They are the ones following the laws."
Opponents have said it will lead to a dangerous mix of booze and firearms.
"It's very dangerous, whether it's concealed or not concealed, " said Pat Sheppard of Hamilton County. "Then if you add alcohol you are adding all kinds of problems."
Businesses don't have to allow the weapons, and facilities home to Ohio's major professional sports teams plan to continue to ban weapons for safety reasons.
The law also allows a person with the proper permit to have a loaded handgun in a vehicle even if the gun is not secured in a holster.