The shuttle, rolling on its giant transporter at less than 2 mph, began the second leg of its trip at 7:15 a.m. PDT from Inglewood, Calif., the Los Angeles Times reported.
The shuttle was scheduled to travel uphill along a street where it would come within inches of apartment buildings on either side.
"It's a very narrow stretch for us," said Marty Fabrick, hired by the California Science Center to lead the move. "Our wings will be over some driveways."
Along Martin Luther King Jr. Boulevard, Endeavor must maneuver around pine trees planted in honor of the civil rights leader, deemed too important to chop down for the shuttle's journey.
"Don't think of the shuttle going nose-first down every street," said LAPD Lt. Andy Neiman. "That shuttle has the ability to zigzag and maneuver, and that's what you're going to see along that route. There may be places where the shuttle is going sideways at an angle."
It's a tight fit, but some areas were open for spectators to watch as the shuttle as it makes its walking-pace journey toward downtown and its new home at the California Science Center in Exposition Park.
The 170,000-pound shuttle required two days to make the journey from the airport to its eventual display location and should arrive at the science center by Saturday evening, officials said.