The G.O.P. has treated Ron Paul as a kook; his son understands which of his views to emphasize and which to downplay. Illustration by Stanley Chow

At 8 A.M. on a Friday in late July, Senator Rand Paul, of Kentucky, stood before a predominantly African-American audience of about a hundred at an Urban League conference in Cincinnati. An ophthalmologist before he was a senator, Paul has spent much of his career in surgical scrubs, but he was dressed nattily, in a charcoal suit and a red rep tie. His typically unkempt curls, which give him the look of a philosophy student lost in thought, were restrained with the help of a hair product. His aides had been promoting the talk for weeks, as part of a yearlong effort to reintroduce himself to political constituencies—on both the left and the right—that may have reason to distrust him. In the next few months, he is planning to deliver a major speech on foreign policy; like race, it is an area in which Paul has encountered strident opposition.

Paul began with the story of Clyde Kennard, a black man in Mississippi who was jailed in 1960 on false charges after he tried to enroll at an all-white college. “Despite our progress,” Paul said, “there are Clyde Kennards today who can’t fully access the franchise because they’re handicapped by either educational or judicial systems.” He laid out a criminal-justice-reform package he has introduced in the Senate to end mandatory minimum-sentencing laws, expunge nonviolent felonies from criminals’ records, reclassify some felonies as misdemeanors, and restore voting rights to citizens who had committed a nonviolent felony. Like Barack Obama, he vowed to free many people imprisoned for crack cocaine, and he announced a new proposal to end the sentencing disparity between crack and powder cocaine. He had even spoken with the President about it—not something about which a Republican would normally boast: “I talked to him last week and said, ‘I will help in any way I can.’ ”

Like many Republicans speaking before a black audience, Paul quoted Martin Luther King, Jr., but he also invoked Malcolm X. He declared, “I support the Civil Rights Act and the Voting Rights Act.” If enacted, Paul’s agenda would arguably do more to address issues that are important to the black community than anything that other members of his party are currently proposing. Cory Booker, of New Jersey, a Democrat and one of only two African-Americans in the Senate, is co-sponsoring part of Paul’s reform package, and Harry Reid, the Democratic Majority Leader, has joined Paul’s bill to restore voting rights to felons. No Republican senator has endorsed any of the legislation. “As a Christian, I believe in redemption,” Paul told the crowd. “And I believe in second chances.”

In some respects, Paul is to Republicans in 2014 what Barack Obama was to Democrats in 2006: the Party’s most prized fund-raiser and its most discussed senator, willing to express opinions unpopular within his party, and capable of energizing younger voters. The Republican National Committee, which in 2008 refused to allow his father, Ron Paul, to speak at its Convention, recently solicited donations by offering supporters a chance to have lunch with Rand Paul. The only potential obstacle to a Paul Presidential candidacy in 2016 is his wife, Kelley. Doug* Stafford, Paul’s top political adviser, said, “Unless Kelley says no, he’s running.” Steve Munisteri, the chairman of the Republican Party of Texas, told me this summer, “He is objectively one of the three most likely people to get the nomination.”

Yet, also like Obama at a similar stage in his career, Paul could be hobbled by past associations and statements, especially on race and foreign policy. He has questioned government attempts, including a core provision of the Civil Rights Act of 1964, to address discrimination in the private sector. He has proposed dramatically slashing the Pentagon’s budget and cancelling all foreign aid. Ron Paul ran for President as the nominee of the Libertarian Party in 1988 and as an isolationist Republican in the Presidential primaries of 2008 and 2012. Rand has followed his lead in opposing most U.S. military interventions of the past few decades, aside from the war in Afghanistan.

Many members of the Republican establishment see him as a dorm-room ideologue whose politics are indistinguishable from his father’s. Earlier this year, Mark Salter, who helped run John McCain’s 2008 Presidential campaign, wrote that Rand’s “foreign policy views, steeped as they are in the crackpot theories that inform his father’s worldview, are so ill-conceived that were he to win the nomination, Republican voters seriously concerned with national security would have no responsible recourse other than to vote for Hillary Clinton.” Paul told me that he wasn’t concerned by such attacks. “Most of the criticism has come from people who would have us involved in fifteen wars right now,” he said. “The American people don’t want that. They’re closer to where I am.”

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After the Cincinnati speech, I drove with Paul across the Ohio River into northern Kentucky, where a series of political meetings were scheduled. Paul is prickly but also has a quick sense of humor. He seemed to relax as we traded stories about the indignities of air travel on our respective trips from Washington. “I got sort of accosted by a guy,” he said. “The aisle people are allowed to stand in the aisle at the end of the flight, not the window people. So the guy behind me in the window gets out, pushes me across, you know, has a hundred-pound belly. When there’s no space between people, the polite thing is not to push yourself in there. He pushes me forward and then leans on me the whole time while we’re waiting the five minutes to get off the plane.”

As I was waiting for Paul to finish a meeting, I told two of his aides about an e-mail that had been sent to reporters during his speech. It was from a public-relations firm working for Ron Paul, also a doctor, who had recently written a column for his Web site explaining why he thought Russia wasn’t responsible for downing Malaysia Airlines Flight No. 17, in Ukraine. “In the interview, Dr. Paul will defend his controversial comments on Putin and voice his support of non-interventionist foreign policy,” the e-mail said. Even as Rand was working to rebrand himself, his father was unintentionally undercutting the effort. Rand’s aides were caught off guard. “It’s good to see that the old man is still out there speaking his mind,” one said.

Paul’s relationship with his father is a sensitive issue. A couple of weeks before his speech to the Urban League, Paul was sitting at a conference table in his Capitol Hill office suite complaining about his press coverage. He was agitated about a story in the Times, earlier this year, which traced his intellectual lineage by reporting on many of the fringe groups and individuals with which his father has been associated during his career, including the John Birch Society and various writers who “championed the Confederacy.”

“I really was disappointed,” Rand said, his voice rising. There was a quote “from some guy who I’ve never met saying something about how slaves should have been happy singing and dancing because they got good food or something. Like, O.K., so now I’m in the New York Times and you’re associating me with some person who I don’t know.” He went on, “It’s one thing to go back and interview my college professor or groups that I actually was with. But I was never associated with any of these people. Ever. Only through being related to my dad, who had association with them.”