In a food processor, pulse basil, pine nuts, garlic, sundried tomatoes, salt and pepper a few times until coarsely chopped. With processor running, slowly add olive oil until combined.
Preheat oven to 400°F.
Place chicken on a greased sheet pan or roasting pan. Completely cover with pesto, lifting skin on top of breast and rubbing underneath the skin as well.
Loosely cover with foil and roast for 30 minutes. Remove foil and continue to roast until a thermometer inserted into the breast reaches 165°F, about 1 hour.
Carve into pieces and serve.
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