Heat the oven to 450°F with a rack in the middle position. On a rimmed baking sheet, toss the chicken with 2 tablespoons of the oil, then season with salt and pepper. Arrange skin side up and roast until the thickest part of the breast (if using) reaches about 160°F and the thickest part of the largest thigh (if using) reaches about 175°F, 30 to 40 minutes. Remove from the oven and let rest for 10 minutes. Meanwhile, in a food processor, combine the avocados, cilantro, jalapeño, onion, vinegar, remaining 2 tablespoons oil and ¼ teaspoon each salt and pepper. Process until smooth, 1 to 2 minutes. Transfer the chicken to a platter and pour over any accumulated juices. Sprinkle with chopped cilantro and serve with the sauce.