Preparation Combine first 5 ingredients in processor. Blend until nuts are finely chopped. Add 6 tablespoons oil and process until well blended. Season with salt and pepper. (Can be made 1 day ahead. Cover; chill. Bring to room temperature before using.) Season chicken with salt and pepper. Heat remaining 1 tablespoon oil in heavy large skillet over medium-high heat. Add chicken; sauté until brown and cooked through, about 6 minutes per side. Transfer chicken breasts to plates. Top each with some pesto and serve.
Preparation Combine first 5 ingredients in processor. Blend until nuts are finely chopped. Add 6 tablespoons oil and process until well blended. Season with salt and pepper. (Can be made 1 day ahead. Cover; chill. Bring to room temperature before using.) Season chicken with salt and pepper. Heat remaining 1 tablespoon oil in heavy large skillet over medium-high heat. Add chicken; sauté until brown and cooked through, about 6 minutes per side. Transfer chicken breasts to plates. Top each with some pesto and serve.