Burnham successfully defended a school teacher, Abigail Betts who had been accused of blasphemy, claiming "Christ was a bastard" and she could prove it through the scriptures.
In 1659 he purchased from Tantonimo (sometimes spelled, Tan-tonimo), Chief sachem of the Potunke Native Americans, a tract of land now covered by the towns of South Windsor and East Hartford, on which he afterward lived, and a part of which is still in possession of his descendants.