It alleges church leaders were aware of the abuse but did not remove Curran or keep him away from children.
Curran worked at St. Christina Parish between 1980 and 1993, and died in 2000.
In 2005, the Archdiocese of Chicago settled lawsuits filed by 24 parishioners who claimed they were abused by priests, including Curran.
Spokeswoman Susan Burritt said the archdiocese had not received a copy of the suit and could not comment.