Buckingham was the only son of Richard Temple-Grenville, 2nd Duke of Buckingham and Chandos, and was educated at Eton and Christ Church, Oxford. He joined the British Army, eventually rising to become a colonel. Buckingham entered politics, as Lord Chandos, in 1846 when he was elected unopposed from Buckinghamshire as a candidate of the Conservative Party. Buckingham served as Member of Parliament from 1846 to 1857, when he resigned. He contested a re-election in 1859, but lost. Buckingham served in various political offices during his tenure.