Henri was the son of Charles Chabot and Henriette de Lur-Saluces. He was the Seigneur of Saint-Aulaye. His great-grandfather was Guy Chabot, a member of old Poitevin nobility, Baron of Jarnac, whose unexpected success in a 1547 duel passed into the French language as the "coup de Jarnac".
On 6 June 1645, Henri married Marguerite de Rohan, sole heiress of the Duke of Rohan and member of the powerful House of Rohan which claimed descent from the old Dukes of Brittany. The couple had six children, three of whom would have further children.