The Vatican named the two men as Francisco Jos Cox Huneeus, archbishop emeritus of the city of La Serena, and Marco Antonio Órdenes Fernndez, archbishop emeritus of Iquique.
Chen, who is on a four-day visit to the Vatican, said he will ask Pope Francis to give his blessings to Taiwan and to pray for cross-strait peace, and he will invite the pope to visit Taiwan next year during a scheduled trip to Japan.
Previously, the Vatican has rarely, if ever, announced laicizations of individual priests and only issued a single-line statement if a bishop had resigned, without further explanation.
Last month Francis defrocked Father Fernando Karadima, an 88-year-old Chilean priest who was accused of sexually abusing teenage boys over many years.
Cox, who is believed to have returned to Germany after a period in Chile, could not be reached for comment.
In May, the Argentine pontiff accepted the resignation of five Chilean bishops amid accusations of abuse and related coverups.
The leaders "shared the hope that the church could live a true rebirth", Pinera said in a statement.
Cardinal Ricardo Ezzati, the archbishop of Santiago, was called to testify about sexual abuse claims.
Scicluna produced a 2,300-page report accusing Chile's bishops of "grave negligence" in investigating the allegations and said evidence of sex crimes had been destroyed.
This decision comes at a hard time for the Catholic church following the newest revelations of widespread sexual abuse within the Church.
They must also refrain from "taking pictures while children, adolescents or vulnerable people are naked, getting dressed or in the shower".