The (New Orleans) Times-Picayune identified the dead person as Zachary Green, 29, an employee at the plant.
Gov. Bobby Jindal said at a news conference 73 people were injured in the blast.
The blast at the Williams Olefins plant occurred at 8:37 a.m., local time, the company said in a statement.
State police said by mid-afternoon the fire at the plant had been extinguished. But police said a control burn was being carried out and a 5-mile perimeter around the plant was still in force.
Todd Stiles, who works at a Honeywell plant about half a mile away, said some of his co-workers reported seeing "a fireball in the air." Thick black smoke continued to billow from the Williams Olefins plant for hours.
Stiles said Honeywell workers were given a choice between sheltering there or evacuating. Workers at other businesses in the area and residents were advised to shelter in place.
Several roads in the area were closed.
The plant's website says it produces about 1.3 billion pounds of ethylene and 90 million pounds of polymer-grade propylene.
The plant is in Geismar, about 30 miles southeast of Baton Rouge and 60 miles west of New Orleans.