Preheat the oven to 350 degrees . In a large pot of boiling salted water, cook the potatoes until just tender, 15 to 20 minutes; drain.
While the potatoes cook, season the chicken with salt and pepper. In a large skillet, heat the olive oil over medium-high heat until hot but not smoking. Add the chicken breasts and cook, turning, until browned, about 3 minutes on each side. Transfer to a large casserole dish.
Add the garlic to the skillet and cook, stirring, until golden, about 30 seconds. Add the tomatoes and their juice and simmer over low heat until the liquid is reduced, 10 to 15 minutes. Add the olives and capers and season to taste with salt.
Scatter the potatoes over the chicken and pour the tomato mixture on top. Bake until the chicken is cooked through, about 25 minutes. Transfer the chicken to a cutting board and slice on an angle. Spoon some sauce and potatoes onto each plate and top with chicken.