The Rev. Gerardo Joannon, who belongs to the Congregation of the Sacred Hearts order, has been relocated to a house for priests in the city of Merlo, Argentina.
The transfer is supposed to be "an act of religious obedience" and a time to pray and serve penance, according to a statement issued by the order. The statement does not give a reason for his penance.
Joannon, who is in his late 70s, publicly admitted last year that he had facilitated illegal adoptions during the 1970s and '80s.
According to the Congregation of the Sacred Hearts order and Chilean authorities, the priest took at least two babies from their biological mothers, either through lies or coercion, and in secret gave them to adoptive families.
Mario Carroza, a prosecutor who investigated the case, said upper-class families would approach Joannon after learning an unmarried daughter was pregnant. He said the priest would then conspire with doctors, nurses, nuns and others to deliver the baby, which would then be raised by the adoptive parents.
"We're talking about crimes like kidnapping, of course, because the baby was taken from the mother without her consent or knowledge; falsification of identity, because the baby was made to appear as a biological child of a different couple, and falsification of documents," Carroza said.
Carroza, though, has ruled the statute of limitations has run out, and that the priest could no longer be prosecuted, angering those still looking for biological parents and children.
The ruling has also puzzled many Chileans who are also questioning the decision to send the priest to Argentina.
CNN tried to get a more elaborate answer from the order, but an interview request was declined. At the house where the priest used to live, another priest hung up the intercom after being asked about Joannon.
The leader of the order, the Rev. Alex Vigueras, was also not answering questions when he arrived at his home. He said "we're not giving any interviews" and quickly drove in and closed the gate.
The Congregation of the Sacred Hearts order conducted an internal investigation last year into the allegations and sent its findings to the Vatican. The Holy See later determined that even though the priest had made ethical and moral mistakes, none of his actions had risen to the level of a violation of canon law.
Carroza, the prosecutor who handled the case, said the investigation is still open and, as more cases surface, he is hoping there will be a case he can prosecute.
Joannon's attorney, Eduardo Novoa, said the crimes his client is accused of were not even on the books until 1988.
"My client, as priest, knew families and would approach them with the intention of giving them support and guidance when unexpected pregnancies occurred," he said.
"In some cases, the grandparents or parents of a young, pregnant woman considered the pregnancy unacceptable and would seek to give the baby away so that another family would raise him as their child."
Chilean authorities said Joannon is only one of many priests, nuns, doctors, nurses and others who conspired to carry out illegal adoptions during the dictatorship of Augusto Pinochet between 1973 and 1990.
The number of stolen children, officials interviewed by CNN said, could be in the thousands. In Chile, they're known as the "Children of Silence."