Heat 1 tablespoon of the oil in a large skillet over medium-high heat. Season both sides of the chicken with salt and pepper. Place the chicken in the hot pan and cook until golden brown and just cooked through, about 3 minutes per side.
Meanwhile, place the pine nuts in a small dry skillet and set over medium heat. Toast the nuts until golden brown, about 3 minutes, shaking the pan frequently to prevent burning. Transfer the pine nuts to a blender or food processor and add cilantro, sour cream, the remaining 1 tablespoon oil, the garlic, and 1/2 teaspoon salt. Process until smooth, adding water, as necessary, to create a thick paste. Serve the chicken with the pesto spooned over the top.