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Bruce Feiler says, in Where God Was Born, page 199-200, the Chaldeans of the Old Testament were an Arabic tribe that migrated northward into central Mesopotamia in about the ninth century BCE and eventually seized control of the kingdom, forming what became known as the neo-Babylonian Empire.
Wikipedia says the modern Chaldean Catholics are in fact Assyrians, originally from northern Iraq, northeast Syria, northwest Iran and southeast Turkey, an area that does not overlap well with the more southern homeland of the Old Testament Chaldeans. Rome initially named the new diocese, formed by those Assyrians who broke from The Assyrian Church of the East and entered communion with the Roman Catholic Church, the Church of Assyria and Mosul. Some 128 years later, in 1681, this was changed to The Chaldean Catholic Church, despite none of its adherents having hitherto used the name 'Chaldean' to describe themselves or their church.
In conclusion, the 'Iraqi Chaldeans' are not ethnically related to the ancient Chaldean people. The name 'Chaldeans' was chosen by the Catholic Church in Rome, although there was no precedent to support this usage.