The man, whose identity was not immediately released, was lying on the tracks when the train ran over him about 5:40 a.m., a police spokesman said.
He was pronounced dead on the scene, officials said.
Police said they do not believe think there was criminality.
Northbound 1 trains were running express from Chambers Street to 14th Street, according to the MTA's website.
2, 3 and southbound 1 trains were running with delays in both directions.
Commuters should allow additional travel time.