Among the traditional list of divine attributes it is commonly said that God is a person. Making a distinction between being a person and having a personality, it is argued that God cannot be a person because it makes no sense to think of him as having a personality. Problems with the notion of divine personality are considered stemming from God's perfection, his infinity, his omniscience, his rationality, his morally good nature and his gender neutrality. Three generic types of response to these problems are considered, but each is found wanting. It is concluded that the problems with personality apply as much to the human case as to the divine.