[verb て-form] 〜て → 〜ちゃ + いけない [verb て-form] 〜で → 〜じゃ + いけない
ちゃいけない is the spoken form of てはいけない, "must not": you say it to forbid something or warn someone off. Take the て-form, turn て into ちゃ or で into じゃ, and add いけない.
The じゃ verbs are the ones whose て-form ends in んで or いで: のむ飲む, あそぶ遊ぶ, しぬ死ぬ, およぐ泳ぐ.
ちゃいけない belongs to conversation with family, friends and children. With いけません it stays casual but sounds gentler, the way a teacher talks to a class. In writing, and to someone above you, use the full てはいけない or てはいけません.