Let R be a Noetherian ring. If R is commutative then (a) every non-unit is contained in a height-1 prime ideal - this is the Krull principal ideal theorem - but (b) R can have an arbitrarily large stable range. The main aim of this paper is to show that if certain non-commutative rings satisfy condition (a) then they have stable range one. We shall prove theTheorem. Let R be a Noetherian domain which is not commutative. Suppose that every non-unit of R lies in at least one height-1 prime ideal and that every height-1 prime is completely prime. Then the stable range of R is one.