Combine milk and eggs in a bowl; whisk to blend well.

In a large heavy-duty resealable plastic food storage bag, combine the flour, salt, and pepper.

Dip a chicken piece in the milk mixture; let excess drip off into bowl.

Put a few chicken pieces in the food storage bag and shake lightly to coat thoroughly. Remove to a plate and repeat with remaining chicken pieces.

Heat oil to 350°. Fry chicken, a few pieces at a time, for about 10 minutes on each side, or until golden brown and cooked through. Chicken breasts will take a little less time than other pieces. Pierce with a fork to see if juices run clear to check for doneness. With a slotted spoon, move to paper towels to drain; sprinkle with salt.