Chetwood sat in the Irish House of Commons as the Member of Parliament for Harristown between 1713 and 1714.
He inherited Harristown, and large properties in Dublin city, from his father-in-law.
He had the reputation for being a shrewd and grasping businessman, and two petitions were presented to the Irish House of Commons complaining about his mismanagement of the Eustace estate.
In 1715 the Provost of Trinity College Dublin complained that Chetwood had refused absolutely to repay debts owing to the college, citing a number of technical legal grounds.
[2] In 1719 his late wife's widowed stepmother and her half-sister, both named Clothilde Eustace, petitioned the Commons complaining that he had refused to pay one her widow's jointure and the other her marriage portion.