It is good to eat the skin with the chicken for the fat content. Otherwise chicken is awfully lean, particularly the white meat. In a low carb diet eating fat is just as important as reducing the carbs (depending somewhat on the goals of the low carb diet). If a person is cutting carbs energy is also being cut. The fat replaces the carb energy. If a person eats only lean meat they end up starving for energy so replacing the carbs with fat is important. Protein makes a very poor energy source but very important for the body's building blocks. Of course once a person is "fat adapted" and trying to lose weight they hope some of the fat and energy will come from body fat. But if a person cuts consumed fat while also cutting consumed carbs the body may interpret it as an energy shortage and go into conservation mode by lowering metabolism, which will be counter productive for fat weight loss.

So it is important to consume enough fat, particularly early on in the journey of cutting carbs mostly out. Body metabolism is important and can change something around 300 calories a day in energy spent. That 300 or so calories difference in metabolism can be the difference between loosing weight and not.