Pelham was the eldest son of Henry Pelham, 3rd Earl of Chichester, and his wife Lady Mary Brudenell, daughter of Robert Brudenell, 6th Earl of Cardigan.
He was educated at Harrow and Trinity College, Cambridge, where he took his degree in 1859.
[1] In 1865 he was elected to the House of Commons for Lewes, a seat he held until 1874.
Lord Chichester married, in 1861, Elizabeth Mary Bligh, only daughter of the Hon.
He was succeeded in his titles by his younger brother Reverend Francis Pelham.