Nobel Peace Prize recipient who was also a sitting President, Theodore "Teddy" Roosevelt (1901, assuming office on the assassination of William McKinley - 1908) received his prize in 1906.

During the election of 1912 he ran as a third party candidate of the Bull Moose Party, losing to Woodrow Wilson (the other Nobel recipient).

Here is a campaign speech he recorded during the 1912 campaign.

Teddy Roosevelt: “The other day in a speech at Sioux Falls, Mister Wilson stated his position when he said the history of government, the history of liberty was the history of the limitation of governmental power. This is true as an academic stigma of history in the past. It is not true as a statement affecting the present.”