Paul, 47, an ophthalmologist who hasn’t held public office, is a favorite of the Tea Party movement. He won an upset victory in the May Republican primary, beating a competitor backed by the state’s party establishment, including Senate Republican leader Mitch McConnell.
With 6 percent of precincts reporting, Paul had 52 percent of the vote and Conway, 41, had 49 percent.
The libertarian-leaning Paul is the son of Representative Ron Paul, a Texas Republican who sought the presidency in 2008 and advocates abolishing the Federal Reserve.
The Tea Party is intent on shrinking the federal government, lowering taxes and rolling back the health-care law pushed by President Barack Obama that was passed earlier this year by the Democratic-controlled Congress.
In the campaign, Paul emphasized spending cuts and said he wants a constitutional amendment requiring a balanced budget.
He favors smaller government and endorsed changes in eligibility requirements for Social Security, as well as for Medicare. He backs term limits for lawmakers.
Paul made early stumbles, drawing criticism after his primary win for calling the White House’s criticism of BP Plc “un-American” after the worst oil spill in U.S. history.
He also attracted national attention when he expressed misgivings about a portion of the Civil Rights Act that forces businesses to serve customers regardless of race, citing his support of property rights.
He will replace retiring Republican Senator Jim Bunning.
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