The Chaldean Catholic Church or the Chaldean Church of Babylon ( , ' ) is an Eastern particular church of the Catholic Church , maintaining full communion with the Bishop of Rome and the rest of the Catholic Church . The Chaldean Catholic Church ( Syriac : ; Ê Ä `` tha kaldetha qÄ thuliqetha , ' ) is an Eastern particular church of the Catholic Church , maintaining full communion with the Bishop of Rome and the rest of the Roman Catholic Church .