Preheat oven to 400°F. Toast pistachios on baking sheet until golden, about seven minutes. Transfer to food processor.

Add cilantro leaves, three teaspoons lemon juice, garlic, and salt to the processor. Pulse to form a paste or pesto. Slowly add 1/2 cup olive oil. Season pesto with pepper.

Gently loosen skin on chicken breasts to form pocket. Spread one tablespoon of pesto under skin and smooth the skin back over it. Sprinkle chicken with salt and pepper.

Heat one tablespoon olive oil in heavy, ovenproof skillet over medium-high heat (on stovetop). Add chicken, skin-side down. Brown about five minutes. Turn chicken over and transfer skillet to oven.

Roast chicken for about 25 minutes.

Place 1/2 cup remaining pesto in a small bowl. Whisk in remaining olive oil and remaining one teaspoon lemon juice. Drizzle pesto sauce over chicken and serve.