He died without male issue and was succeeded (in the earldom according to the special remainder) by his nephew Arthur Chichester, the second Earl. He was the eldest son of Lieutenant-Colonel John Chichester, second son of the first Viscount. Lord Donegall had previously represented Donegal County in the Irish House of Commons. His eldest son, the third Earl, was a Major-General in the Spanish army and fought in the War of the Spanish Succession. He was killed in action in 1706. His eldest son, the fourth Earl, died childless and was succeeded by his nephew, the fifth Earl. He was the son of the Hon. John Chichester, younger son of the third Earl. Lord Donegall was created Baron Fisherwick, of Fisherwick in the County of Stafford, in the Peerage of Great Britain in 1790, and one year later he was further honoured when he was made Earl of Belfast and Marquess of Donegall in the Peerage of Ireland.