Open carry has been resisted by law enforcement groups, but sailed through the Senate on a 20-10 vote. Republican Gov. Greg Abbott has pledged to sign an open carry bill if one reaches his desk.
Texas already allows concealed carry of handguns but is one of just six states that ban open carry.
The bill allows open carry of handguns in shoulder or belt holsters. Licensing would the same as concealed handguns, including background checks, classroom and firing range instruction.
The Senate is expected to vote Wednesday on a bill allowing concealed handguns in college classrooms and buildings.
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