"I have waited for that moment for such a long time, and it was kind of a shock," Tomlinson said last Thursday. "I have watched for so long and I looked up and to see him right in front of me, you just kind of shake your head and realize that it's Jim Brown.
"It was an incredible feeling, just one of the best moments in my life."
In 5½ NFL seasons with the Chargers, Tomlinson already has created a lifetime of great on-field moments, but this off-field encounter was special. Growing up in Rosebud, Texas, part of Tomlinson's motivation to become a running back came from watching video of Brown's smashing, crashing exploits with the Cleveland Browns.
The meeting between Brown, who is a special consultant to the Browns, and Tomlinson was appropriate, for they are on a collision course in terms of history.
On Sunday in Cincinnati, Tomlinson went off. He tied a career high by scoring four rushing touchdowns in San Diego's manic 49-41 victory over the Bengals. Two of those scores came in a span of 15 seconds after a Carson Palmer fumble. Tomlinson, in just 88 career games, has now scored a staggering 98 touchdowns. The fastest ever to 100? Brown and Emmitt Smith both hit the century mark in 93 games.
If Tomlinson can score just two TDs in his next four games -- he is averaging 1.1 per game over his career -- he will break that mark. The way he's going, he will shatter it. Tomlinson has now scored 15 touchdowns in his last five games. The previous record-holder for touchdowns in a five-game span? Brown, naturally, with 14 in 1958.
Three days before the game in Cincinnati, Tomlinson talked about what it would mean to beat Brown and Smith to 100 touchdowns.
"Honestly, I don't know how to feel about it," Tomlinson said. "What an incredible player [Brown] was, the guy who inspired me to become a running back. Seeing him and Emmitt Smith come along -- being from Texas and Emmitt playing for the Cowboys and seeing most [of] his games -- I would say as a kid [it's] a dream come true to be the fastest to reach 100.
"As a kid in a country town, it's almost a fairy tale."
The end zone in the NFL is real estate more precious than any slice of land in Manhattan, Maui or Beverly Hills. And Tomlinson, who is listed at 5-foot-10, 221 pounds, but appears closer to 5-8, 215, gets there more often than anyone in football. No one has scored more touchdowns in the last five seasons than L.T.
Consider the Hall of Fame-quality names he is vaulting on the all-time list. Before Sunday's game, he was tied for 21st with Jerome Bettis and Priest Holmes at 94 touchdowns. Now they're in the rearview mirror. Soon to join them is Eric Dickerson, who scored 98 touchdowns. Tomlinson will next pass Franco Harris and Curtis Martin (100) and Steve Largent (101).
And he's only 27 years old.
"There is something about that little white strip, the goal line, that makes you give an extra 110 percent," Tomlinson said.
Tomlinson has scored 18 touchdowns, 16 rushing and two receiving, and leads the NFL in scoring with 108 points. Bears place-kicker Robbie Gould, with 23 field goals and 29 extra points, is second with 98. Tomlinson also leads the NFL in total yards from scrimmage (1,309) and is 39 yards behind Tiki Barber's league-leading rushing total of 971 yards.
And it isn't just the frequency of Tomlinson's touchdowns; his versatility is also unrivaled. The breakdown: Tomlinson has run for 88 touchdowns, caught 10 as a receiver and even thrown five for scores.
"There is something about that little white strip, the goal line, that makes you give an extra 110 percent."
LaDainian Tomlinson on scoring TDs
"He gets the pitch and you see all the corners and safeties coming up to try and make the tackle and -- boop! -- he lays the ball right over," said fullback Lorenzo Neal. "He is not a double threat, he is a triple threat."
Said quarterback Philip Rivers, "He just has a knack for throwing on the run. Whenever we work on that stuff in practice, it's awesome to see."
Is Rivers worried about losing his job?
"No," he said, smiling, "not really. He's dangerous when he's back there throwing because he can run it. We are not swapping spots, that's for sure."
According to Neal, Tomlinson does not recalculate his place in history after every touchdown. He is, Neal said, fairly oblivious to the growing body of numbers he has produced. In this era of me-first players, Tomlinson is a genuinely modest throwback.
"Watch the end of his runs, and there are four, five guys celebrating with him in the end zone," Neal said. "Because he is a guy that is so humble."
In 1960, the Packers' Paul Hornung scored 176 points -- 15 touchdowns, 41 extra points and 15 field goals -- a record that still stands 46 years later. Second on the all-time list, with 168, is Seattle's Shaun Alexander, who set a league record last season with 28 touchdowns.
These unprecedented numbers are within Tomlinson's reach. At an even two touchdowns per game, he is on pace to score 32 touchdowns -- good for 192 points.
What is he thinking when he crosses the goal line?
"You're happy because you just put points on the board," Tomlinson said. "You are happy for a few quick seconds, then you go back to being focused on what is going to happen next."
Which, these giddy days in San Diego, is usually another touchdown.
Greg Garber is a senior writer at ESPN.com.