Preheat oven to 350 degrees. Sprinkle salt and pepper on each side of the chicken breasts and place into the skillet, add the lime juice on top of the breasts. Sear on each side for 3-4 minutes.

Chop the fresh cilantro and mix together with ¾ cup of the sour cream, spread ¼ of the mixture on the bottom of a baking dish. Place the chicken breasts into the baking dish, spread ½ of the sour cream mixture on top of the chicken breasts. Cover with foil and bake for 35-40 minutes, or until the chicken is tender. With 10-15 minutes left for the cooking time is up, remove the foil.

Mix together the extra sour cream, should be ¼ of a cup, and the milk together. Serve on top of the plated chicken breasts. Garnish with additional cilantro.