Heat 1 inch vegetable oil in large deep skillet over medium-high heat until deep-fry thermometer registers between 350°F and 375°F. Fry chicken a few pieces at a time so oil doesn’t cool down. Turn chicken to brown evenly and remove when golden and cooked through. Wings should take 10 to 15 minutes, drumsticks 15 to 20 minutes, breasts and thighs 20 to 25 minutes. Chicken is done when meat thermometer inserted in center reaches 170°F. Drain on wire rack to keep chicken crispy.
TIP: Don’t have a deep-fry thermometer? You can tell when oil is hot enough with a wooden spoon. Stick spoon into oil so that handle touches bottom of pot. Oil will bubble around handle when it’s hot enough for frying.