Heat olive oil in heavy medium skillet over medium-high heat.
Sprinkle chicken breast halves with salt and pepper.
Add chicken to skillet and cook until golden and cooked through, about 5 minutes per side.
Transfer to plate.
Add chopped shallot to same skillet; sauté 30 seconds. Stir in tomatoes, white wine, capers, and caper brine. Boil until tomatoes release juices, about 4 minutes. Stir in chopped basil. Season sauce with salt and pepper. Return chicken to skillet. Cook until warmed through, spooning sauce over chicken, about 1 minute.