He was the great-great-great-grandson of John Chichester, grandson of Edward Chichester, 1st Viscount Chichester, and younger brother of Arthur Chichester, 2nd Earl of Donegall.
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He was the eldest son of Edward Chichester, 1st Viscount Chichester, and made a career as a soldier before being elected to the Irish House of Commons as Member of Parliament for Armagh in 1634 and again in 1640.
On 11 September 1761, he married Lady Anne Hamilton, daughter of James Hamilton, 5th Duke of Hamilton.
Born William Hanbury at Kelmarsh, he was the son of William Bateman-Hanbury, 1st Baron Bateman and his wife Elizabeth, daughter of Lord Spencer Chichester, son of Arthur Chichester, 1st Marquess of Donegall.