Heat oven to 400 degrees Fahrenheit. In heavy, oven-proof iron skillet, heat 1 tablespoon olive oil. Season skin side of chicken breasts with salt and pepper. Add butter to skillet; add chicken breasts, skin side down. Add leek pieces, tomatoes, peppers, and garlic to pan.
Season skinless side of chicken with salt and pepper.
After about 4 minutes, when skin side is crisp, turn breasts over. Add 3 sprigs of rosemary to pan. Place, uncovered, in oven; roast for 50 minutes, checking each 20 minutes; add 1/4 cup water or broth as needed to keep vegetables moist.
Remove pan from oven. Add 1/4 cup water or broth to pan; stir.
Slice chicken and serve surrounded by roasted vegetables. Drizzle with pan juices and olive oil. Sprinkle with salt and pepper.