Let (k, P k ) be an ordered field and Γ be a dense additive subgroup of R. In this paper, we shall construct a noncommutative ordered division ring (D, P) and a compatible valuation υ on (D, P) such that (i) the value group of υ is Γ and (ii) the residue division ring (D v , P v ) is order isomorphic to (k, P k ). This problem is interesting because, in effect, we are constructing the "simplest" or in some sense the smallest noncommutative ordered division ring.