Try to live on zero carbs for a few weeks. And by zero I mean zero. Just chicken breasts and water and vitamin supplements. You will be miserable and ill.
Miserable maybe, but ill, maybe, but only because, chickens, as with other small game, do not provide all the essential fatty acids that the human body requires. There are enough essential amino acids in chicken. Lack of carbs won't kill you. You would be healthier without eating carbs.