This paper examines coalition formation problems from the viewpoint of mechanism design. We consider the case where (i) the list of feasible coalitions (those coalitions which are permitted to form) is given in advance; and (ii) each individual's preference is a ranking over those feasible coalitions which include this individual. We are interested in requiring the mechanism to guarantee each coalition the "right" of forming that coalition at least when every member of the coalition ranks the coalition at the top. We name this property coalitional unanimity. We examine the compatibility between coalitional unanimity and incentive requirements, and prove that if the mechanism is strategy-proof and respects coalitional unanimity, then for each preference profile, there exists at most one strictly core stable partition, and the mechanism chooses such a partition whenever available. Further, the mechanism is coalition strategy-proof and respects coalitional unanimity if, and only if, the strictly core stable partition uniquely exists for every preference profile.