In a food processor, combine the herbs with the garlic, pine nuts, capers, vinegar and 12 cherry tomato halves; pulse until chopped. Add 3 tablespoons of the olive oil and pulse just until pureed. Season with salt and pepper.
Heat 1 1/2 tablespoons of the remaining olive oil in each of 2 large skillets. Season the chicken with salt and pepper and cook over high heat, turning once, until golden on both sides, about 5 minutes. Transfer to a platter, cover loosely with foil and keep warm.
Return 1 of the skillets to the heat, add the remaining tomatoes and cook over high heat just until heated through, about 1 minute; season with salt and pepper. Spoon the tomatoes over the chicken and serve the pesto on the side.