Sprinkle chicken with salt and pepper on both sides. Cook over medium heat in a grill pan or gas grill, turning once, about 10 minutes total. Let chicken cool, and then cut into thin slices. Cut slices into slivers.
Cook bacon in microwave until crisp; let cool completely on a paper towel.
In a large salad bowl, combine Swiss cheese, Cheddar cheese, pepperoni, radish, tomato, cucumber and carrot. Add chicken, lettuce, oil and vinegar. Toss well, crumble bacon on top and toss again. Serve immediately.