It is well-known that feature structures (Rounds and Kasper 1986) can be fruitfully viewed as forming a Scott domain (Moshier 1988). Once a linguistically motivated notion of "set value" in feature structures is countenanced, however, this is no longer possible inasmuch as unification of set values in general fails to yield a unique result. In Pollard and Moshier 1990 it was shown that, while falling short of forming a Scott domain, the set of feature structures possibly containing set values satisfies the weaker condition of forming a "2/3 SFP domain" when equipped with an appropriate notion of subsumption: that is, for any finite setS of feature structures, there is a finite setM of minimal upper bounds ofS such that any upper bound ofS is approximated by a member ofM. Unfortunately, the 2/3 SFP domains are not as pleasant to work with as Scott domains since they are not closed under all the familiar domain constructions; and the question has remained open whether the feature structure domain satisfies the added condition of profiniteness. (The profinite ω-algebraic domains with least elements are a subclass of the 2/3 SFP domains which enjoy the pleasant property of being the largest full subcategory of ω-algebraic domains that is closed under the usual domain constructions.) In this paper we resolve this question in the affirmative.