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I am descended from Willis and Sophia H. Chase. It is thought that Sophia was a Hoag; her property transaction with Arnold C. Hoag is a strong suggestion. Best we can tell, Arnold is the grandson of Elliot, brother of Cardinal Hoag.
Looks like both Arnold's family and his father's family (Isaac) relocated to Branch, MI about 1858.
If this is of interest, I am willing to exchange information.