Preheat oven to 350° F.

In a baking pan toast pecans in one layer in middle of oven until golden and fragrant, about 10 minutes. With a sharp knife cut peel and pith from oranges and cut orange sections free from membranes. Discard outer leaves from radicchio and halve lengthwise. Cut radicchio crosswise into 1/8-inch-thick slices.

Cut bacon into 1/2-inch pieces and in a 12-inch heavy skillet cook over moderate heat, stirring, until just golden, with slotted spoon transfer bacon to a large bowl. Pour off fat from skillet and in skillet heat oil over moderately high heat until hot but not smoking sauté radicchio, stirring, until wilted, about 5 minutes. Reduce heat to moderate and stir in vinegar. Cook radicchio, stirring, 1 minute more. Transfer radicchio to bowl and toss with bacon, nuts, and pepper. Season salad with salt.

Serve salad topped with orange sections.