cannot do without; indispensable; absolutely necessary
Used when something is essential and cannot be omitted. Often follows a noun marked with が or は.
See also: なくてはいけない
この仕事には経験が無くちゃいけない。
Experience is indispensable for this job.
健康は無くちゃいけないものだ。
Health is something you cannot do without.
Attaches to the negative stem of a verb (ない-form minus ない) to express obligation. Colloquial contraction of なくてはいけない.
See also: なくてはいけない
もう行かなくちゃいけない。
I have to go now.
I must do my homework.
Both 無くちゃいけない and なきゃいけない are casual contractions expressing obligation, but 無くちゃいけない derives from なくては while なきゃいけない derives from なければ.
Contraction of なくてはいけない, from 無い (ない, 'not exist') + ては + いけない ('must not'). The ては contracts to ちゃ in casual speech.