In the 450 million peso ($900,000) suit, Juan Carlos Cruz, James Hamilton and Jose Andres Murillo accuse the church of negligence for initially ignoring their complaints about the priest.
“We really want to establish the responsibility of the church,” Cruz said.
The compensation, if granted, would be donated to charity.
The case against Karadima, who trained many of the priests who took leadership positions in the Chilean Catholic Church, was dismissed in December 2010 because the 10-year statute of limitation on such crimes had expired.
But it was reopened in March 2011 after the Vatican found the priest guilty of sexual abuse of minors and sentenced him to a life of prayer.
In November 2011, a Chilean judge ruled that Karadima had engaged in sexual abuse of three minors in the past but could not be tried because the statute of limitations had run out.
Karadima has denied committing any abuse.