After more review, James is not the father of My Great Great Grandfather. I found James Chamberlain on the 1870 US Census which states he was married to Hannah Chamberlain born in 1801 in Vermont. The mother of Augustus Young Chamberlain was also born in Vermont around 1801, however she was a widow on the 1850 US Census. Which means that she is not the same Hannah Chamberlain that is married to James in 1870.
Additional information: Augustus's sister is Emma E Bull (2nd wife to Hiram C Bull) born in 1828. Augustus's brother is Edward Payson (E.P.) Chamberlin Jr of Atlanta, a wealthy businessman. Augustus married Mary Ann Esterly of Whitewater, WI, daughter of George Esterly (founder of Esterly Manufacturing company). I hope this additional information helps make a connection to who Augustus's Father was.