A Semitic people, the Chaldeans migrated to southern Mesopotamia (possibly from the Arabian desert) in the first millennium B.C. The Chaldeans appear in Assyrian royal inscriptions from the 9th century. The Chaldeans are associated with the city of Ur and the Biblical patriarch Abraham. Chaldeans ruled Babylonia from about 625-538 B.C. when the Persian King Cyrus the Great invaded. The Chaldeans' rule started when Nabopolassar pushed the Assyrians out of Uruk.
Sources: "Chaldean" A Dictionary of World History. Oxford University Press, 2000, and "Chaldeans" The Concise Oxford Dictionary of Archaeology. Timothy Darvill. Oxford University Press, 2008.
"Arabs" in Babylonia in the 8th Century B. C.," by I. Ephʿal. Journal of the American Oriental Society, Vol. 94, No. 1 (Jan. - Mar., 1974), pp. 108-115.