Francis Wemyss Charteris, Lord Elcho (31 January 1749 – 20 January 1808) was a Scottish nobleman and Member of Parliament.
He was the only son of the Honourable Francis Charteris, second son of James Wemyss, 5th Earl of Wemyss. The fifth Earl's eldest son David Wemyss, Lord Elcho had been attainted for his part in the Jacobite Rising of 1745 so after the Earl's death in 1756 the earldom became forfeit.
Charteris was elected to Parliament for the Haddington district of burghs in 1780. From 1784 he was in opposition to the government of William Pitt the Younger.
In 1787 Charteris' uncle Lord Elcho (who but for his attainder would have been 6th Earl of Wemyss) died. As Charteris' father had not been attainted himself, he assumed the title as 7th Earl of Wemyss, with Charteris assuming the title Lord Elcho. At the time eldest sons of Scottish peers were not allowed to represent Scottish constituencies in Parliament, and after a debate on the matter Charteris had to vacate his seat. Although it was later established that the Earldom of Wemyss remained forfeit and his father was not after all a Scottish peer, Charteris did not attempt to re-enter Parliament.
Charteris died on 20 January 1808 at Amisfield House, East Lothian, and was interred at St Mary's Collegiate Church, Haddington.
Francis Charteris married in 1771 Susan, daughter of Anthony Keck and granddaughter of James Hamilton, 4th Duke of Hamilton. They had one son and four daughters: