Cameron and Calcasieu parishes are reporting severe damage from high winds and storm surge.
Glass walls in buildings in Lake Charles were shatttered.
Nearly 609,000 homes and businesses have no power across Louisiana, Texas and Mississippi.
Early reports said Texas appeared to have escaped major damage from the hurricane.
The first death caused by Laura was reported about 8 a.m. CDT. A 14-year-old girl was killed when a tree fell on her home in Leesville, Louisiana, according to the governor’s office. Leesville, in Vernon Parish, is about 95 miles inland.
The storm made landfall at 1 a.m. CDT Thursday near Cameron, Louisiana, where an estimated 150 people in the surrounding parish had refused to evacuate, according to the Associated Press. Some planned to ride out the storm in elevated homes, while others were reportedly in recreational vehicles.
“As we wake up today, everyone must remember that the threat #Laura poses to Louisiana is ongoing. Stay home, continue to heed the warnings and instructions of local officials and monitor your local news to stay informed,” tweeted Louisiana Gov. John Bel Edwards.
In Calcasieu Parish, the parish just to the north of Cameron, Dick Gremillion, director of emergency management, told The Weather Channel there was “a lot of tree damage, a lot of utility damage.”
Power outages were skyrocketing in Louisiana, Texas and Mississippi as the storm carved its way inland. Nearly 609,000 customers were without electricity by 9 a.m., according to poweroutage.us.
Early reports before the sun came up could only hint at the devastation. Images shared on social media showed buildings in downtown Lake Charles, Louisiana, with every window blown out. One storm chaser said the falling glass had injured some people. Lake Charles is about 45 miles north of where Laura made landfall.
Another image showed high winds tipping over a large RV camper. The transmission tower for Lake Charles TV station KPLC collapsed into a heap like a bunch of Tinkertoys.
The first daylight video from a drone showed homes surrounded by water with shingles stripped off roofs. Giant pine trees lay across other houses. As the drone flies over a motel, you can see through exposed rafters into the second-floor rooms.
“Wait to come home. Wait. I know everybody wants to come back and clean up their yards, but there’s no electricity and no water,” Guillory told KPLC.
“As I ride around it is bad all over. This is going to be down for a while. It’s hit us hard,” he said.
Guillory rode out the hurricane in a government building in Lake Charles. He said the building started swaying about 2 a.m. as it was buffeted by Laura’s high winds. He said some of the people who chose not to evacuate began calling for help about that time.
“People are calling the building but there ain’t no way to get to them,” he told The Associated Press, adding he hoped they could be rescued later Thursday if the roads were passable.
Parts of Interstate 10 in Louisiana were shut down late Wednesday night ahead of anticipated flooding from Hurricane Laura.
Gov. Bel Edwards tweeted that the interstate was closed eastbound at the Texas-Louisiana state line and westbound from the Atchafalaya Basin. The closure affects an estimated 120 miles of that interstate.
As the storm intensified on approach late Wednesday, Bel Edwards could only speak bleakly.
“I will tell you we are certain that at this time tomorrow we will be doing search-and-rescue for a large number of individuals, many of whom are going to need to require sheltering after that for some period of time before they can go home,” he told Fox News.
Texas appeared to have escaped widespread damage, KHOU reported.
Orange, Texas, along the Sabine River on the border with Louisiana, was one of the hardest hit areas. Mayor Larry Spears told KTRK trees were down, streets were littered with debris and some businesses lost roofs, but he expected much worse.
Video on KHOU showed a church in Orange that was damaged by the storm.
Highway 87 on the Bolivar Peninsula in Galveston County was covered with rocks that Laura dumped on the roadway. The county and the cit of Galveston lifted their mandatory evacuation orders.