The Earl of Chatham was William Pitt the Elder (1708-1778), the Secretary of State who directed Britain's involvement in the Seven Years War and the Prime Minister who gave the city of Pittsburgh its name. He collapsed in the House of Lords on 7 April 1778, during a debate on the American War of Independence. He died at home the following month.
The painting (1779), by American artist John Singleton Copley, depicts Pitt's collapse (not death). It hangs in the National Portrait Gallery, and a high resolution image can be found here.