Adam Clarke on 2 Samuel 19:37

Thy servant Chimham - It is generally understood that this was Barzillai's son; and this is probable from 1Kgs 2:7, where, when David was dying, he said, Show kindness to the sons of Barzillai: and it is very probable that this Chimham was one of them. In Jer 41:17 mention is made of the habitation of Chimham, which was near to Bethlehem; and it is reasonably conjectured that David had left that portion, which was probably a part of his paternal estate, to this son of Barzillai.