It was during his first re-election campaign in 1984, when he defeated Democratic former Gov. William Winter. Since then, Cochran has easily defeated challengers who've had difficulty raising money or gaining traction.
Cochran, who turns 76 in December, is expected to announce late this year whether he'll seek a seventh six-year term in 2014. Though he's holding nearly $804,000 campaign cash, he's keeping his decision — if there is one yet — a closely guarded secret.
A longtime leader of the Appropriations Committee, Cochran has brought billions of dollars to Mississippi. The money has gone into military bases, universities, local schools, highways, bridges, agriculture projects, disaster recovery and a wide variety of other projects large and small.
The federal spending has made Cochran lots of friends in lots of places, crossing traditional dividing lines of party, race and geography. It has also brought sharp criticism from people who see it all as pork.
If Cochran runs in 2014, he'll face a tougher challenge than he's had the past three decades, and it's coming from within the Republican Party.
An estimated 300 to 400 people turned out at the Jones County Courthouse in Ellisville on Oct. 17 to watch second-term state Sen. Chris McDaniel announce he's running for U.S. Senate next year, regardless of what Cochran does.
McDaniel is a 41-year-old attorney with perfect posture, clear enunciation and a penchant for quoting Winston Churchill and even John F. Kennedy. He's a suit-and-tie kind of guy whose tea party conservatism appeals to 44-year-old Chris Gonthier of Sumrall. Like several others at the McDaniel event, Gonthier was wearing a purple T-shirt with a slogan on the front, in yellow: "Yes! Obama, the Constitution does matter. Leave our rights alone." On the back was an image of President Barack Obama's face in a circle with a slash through it and the words: "Just say no. November 2012."
"Our government is out of control," said Gonthier, a Baptist pastor. "It's no longer, 'We, the people.' It's, 'They, the bureaucrats.'"
If Cochran doesn't run, several high-profile politicians are expected to jump into the Senate race, including Republican Secretary of State Delbert Hosemann.
"If he decides to run again, I'm going to support him," Hosemann said of Cochran. "If he decides not to run, I do have an interest in the Senate."
State Auditor Stacey Pickering, 3rd District U.S. Rep. Gregg Harper and Lt. Gov. Tate Reeves are frequently mentioned as other possible Republican contenders if Cochran opts out.
As for the Democrats? State party chairman Rickey Cole told The Associated Press: "We fully expect that Sen. Cochran will run for re-election and in the very likely event that he does, we don't foresee a major Democratic challenger emerging.... When you have an incumbent like that, a challenge is an uphill battle."
If Cochran stays home, some Democrats' names that pop up are former Gov. Ronnie Musgrove, former 1st District U.S. Rep. Travis Childers and Ocean Springs Mayor Connie Moran.
Cochran was an Ole Miss cheerleader as an undergrad in the 1960s and is an attorney, piano player, state history aficionado and member of the Smithsonian Institution Board of Regents. He's such a fixture in Mississippi politics that he's on the short list of politicians instantly recognizable by first name only. McDaniel will run a serious campaign with impassioned support from conservatives who are deeply skeptical of big government. But the Thad brand would be tough for any challenger to defeat.
(Daily Corinthian columnist Emily Wagster Pettus is a writer for the Associated Press based in Jackson.)