Chetwynd was the eldest son of John Chetwynd of Ingestre and his wife Lucy Roane, daughter of Robert Roane of Tullesworth, Chaldon, Surrey, and was baptized on 3 June 1678.
In 1693 he succeeded to the Ingestre estates on the death of his cousin Walter Chetwynd (1633–1693).
He was educated at Westminster School from 1692 to 1696 and matriculated at Christ Church, Oxford on 28 May 1696, aged 18.
[2] Chetwynd was returned unopposed as Member of Parliament for Stafford at a by-election on 26 December 1702 on the death of his father.
In 1717 he was elevated to an Irish Peerage as Viscount Chetwynd, with special remainder to his father's descendants.