Right to Work laws prevent a worker from being forced to pay union dues as a condition of employment.
Backed by dozens of Republican legislators and business leaders in a Capitol Annex hearing room, the House's top Republican acknowledged the issue is controversial.
A Right to Work initiative by Gov. Ernie Fletcher in 2006 sparked union protests. In 2011, labor activists swarmed the Indiana State Capitol.
Union members descended upon Hoover's news conference on Thursday.
Supporters say it's about making Kentucky more competitive as the state loses thousands of jobs to other states that now have Right to Work laws. 25 other states already have such laws, including Indiana and Tennessee.
Right to Work is also an issue in Kentucky's U.S. Senate race. Republican incumbent Mitch McConnell and GOP challenger Matt Bevin favor the idea.