With the mapping of the human genome, genetic privacy has become a concern to many. People care about genetic privacy because genes play an important role in shaping us--our genetic information is about us, and it is deeply connected to our sense of ourselves. In addition, unwanted disclosure of our genetic information, like a great deal of other personal information, makes us vulnerable to unwanted exposure, stigmatization, and discrimination. One recent approach to protecting genetic privacy is to create property rights in genetic information. This Article argues against that approach. Privacy and property are fundamentally different concepts. At heart, the term "property" connotes control within the marketplace and over something that is disaggregated or alienable from the self. "Privacy," in contrast, connotes control over access to the self as well as things close to, intimately connected to, and about the self. Given these different meanings, a regime of property rights in genetic information would impoverish our understanding of that information, ourselves, and the relationships we hope will be built around and through its disclosure. This Article explores our interests in genetic information in order to deepen our understanding of the ongoing discourse about the distinction between property and privacy. It develops a conception of genetic privacy with a strong relational component. We ordinarily share genetic information in the context of relationships in which disclosure is important to the relationship--family, intimate, doctor-patient, researcher-participant, employer-employee, and insurer-insured relationships. Such disclosure makes us vulnerable to and dependent on the person to whom we disclose it. As a result, trust is essential to the integrity of these relationships and our sharing of genetic information. Genetic privacy can protect our vulnerability in these relationships and enhance the trust we hope to have in them. Property, in contrast, by connoting commodification, disaggregation, and arms-length dealings, can negatively affect the self and harm these relationships. This Article concludes that a deeper understanding of genetic privacy calls for remedies for privacy violations that address dignitary harm and breach of trust, as opposed to market harms, as the property model suggests.