Place each chicken breast half between 2 sheets of heavy-duty plastic wrap; pound to 1/2-inch thickness using a meat mallet or rolling pin.
Heat oil in a large nonstick skillet over medium-high heat. Sprinkle the chicken with salt and pepper. Add chicken to pan; cook 2 minutes on each side or until done. Remove from pan.
Add shallots to pan; sauté 1 minute or until tender. Combine broth and cornstarch, stirring with a whisk. Add broth mixture, capers, juice, and tarragon to pan. Bring to a boil; cook until reduced to 1/2 cup (about 3 minutes), stirring frequently. Serve sauce over the chicken.