The institution of consanguineous marriage - a marriage contracted between close biological relatives - has been a basic building block of many societies in different parts of the world. This paper argues that the practice of consanguinity is closely related to the practice of dowry, and that both arise in response to an agency problem between the families of a bride and a groom. When marriage contracts are incomplete, dowries transfer control rights to the party with the highest incentives to invest in a marriage. When these transactions are costly however, consanguinity can be a more appropriate response since it directly reduces the agency cost. Our model predicts that dowry transfers are less likely to be observed in consanguineous unions, and that close-kin marriages are more prevalent at both extremes of the wealth distribution. An empirical analysis using data from Bangladesh delivers results consistent with the predictions of the model, lending strong support to our theory.