Monsignor William Lynn is the first U.S. church official charged for allegedly keeping accused priests in ministry.
The 61-year-old Lynn is scheduled for trial with the Rev. James Brennan and former priest Edward Avery, both charged with rape.
Jury selection may take several weeks. Lynn was in court with his lawyers Tuesday, when the court delayed the start of jury selection without explanation.
They are due back in court Wednesday.
Prosecutors say Lynn knew about secret files at the archdiocese that held child sex-assault complaints lodged against dozens of priests.
Lynn's lawyers say he took orders from the late Cardinal Anthony Bevilacqua from 1992 to 2003.