But some people decided to get an up-close look. A few actually joined the chase on the freeways. Others cheered from sidewalks and overpasses.
Simpson was wanted in the slayings of his ex-wife, Nicole Brown Simpson, and her friend, Ronald Goldman. Simpson was supposed to turn himself in that day but didn't show up to police headquarters to surrender.
The chase, which occurred 20 years ago today, began in Orange County and ended at Simpson's Brentwood home.
Here are some snippets from The Times' coverage that day of people wanting to be a part of history:
Most were glued to television sets when they realized that the pursuit would be passing near them, so they said they jumped in their cars and positioned themselves on on-ramps or along the freeway so they could join in.
"We thought it would be therapy for O.J. if he saw motorists honking and bunching up behind him," said Steve James of Diamond Bar, who joined the pursuit in Anaheim.
The harrowing chase started around 6 p.m., when law enforcement authorities traced the Bronco to Orange County by following cellular phone transmissions from the truck. By 7:15, after several tries, officers started talking to the Bronco's occupants on the car phone. They were not the only callers. Radio listeners took to the airwaves and urged the onetime football hero to give himself up.
Shortly before 8 p.m., as Simpson's vehicle left the freeway at Sunset Bouelvard, near his estate, people were waiting in the middle of the street, some lunging toward the vehicle.
A large, boisterous crowd gathered at Rockingham Avenue and Sunset as the drama wound down, some of them cheering and chanting, "Free O.J." Others held signs saying "Save the Juice" and "We Love the Juice." About 50 young people tried to clamber over an ivy-covered hillside leading to the Simpson home, but police pushed them back.
"I just wanted to make sure he didn't commit suicide," said Brian Washington, 25, who drove down from Lancaster with his pregnant wife. "Let's just go on from here. You've got young and old out here and we are all pulling for him."
Todd Gibson, 21, drove up from Orange County after spotting Simpson on the freeway. Holding a sign that said "Go O.J.," he wanted to get one last glimpse of his hero, he said.
"This is the most incredible thing in my entire lifetime," Gibson said. "For him to go down like this, well, it's just not right."
Brochelle Hale, 35, of Hawthorne said she was glad when Simpson finally surrendered.
"It doesn't make any sense for him to go through all he has gone through," she said. "He should have turned himself in at the beginning. He ain't no hero."
In general, though, the mood was festive, and in almost every case, supportive of Simpson.
"The Juice is loose!" several people shouted.