BNSF Railway spokesman Joe Faust said his company's train hit the van in Red Banks, about 40 miles (65 kilometers) southeast of Memphis, Tennessee.
Marshall County Coroner James Richard Anderson said a woman and a man riding in the back seat of the van were killed. He's not releasing their names yet. Local news outlets reported they were Tennessee residents. The state line is about 12 miles (20 kilometers) to the north.
Anderson said one of the injured was taken to a hospital in Olive Branch, and two others to a hospital in Memphis.
The white van crumpled on impact and was pushed off the tracks by the train, which Faust said was carrying chemicals south from Castleton, North Dakota, to Birmingham, Alabama.
Members of the train crew were not injured.
Anderson said it wasn't clear whether the van was moving or stationary on the crossing, which has lights and bells but no gates. Anderson said the van belongs to a business. It's unclear whether the occupants are employees.
Federal Railroad Administration records show no crashes at the crossing in recent years. Records show 10 trains a day travel down the track, reaching speeds as fast at 60 mph (95 kph).
Faust said the train's lead locomotive has a camera and the railroad will share video with local law enforcement and the Federal Railroad Administration as each investigates the crash.
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