Peer production projects like Wikipedia have inspired voluntary associations, collectives, social movements, and scholars to embrace open online collaboration as a model of democratic organization. However, many peer production projects exhibit entrenched leadership and deep inequalities, suggesting that they may not fulfill democratic ideals. Instead, peer production projects may conform to Robert Michels' "iron law of oligarchy," which proposes that democratic membership organizations become increasingly oligarchic as they grow. Using exhaustive data of internal processes from a sample of 683 wikis, we construct empirical measures of participation and test for increases in oligarchy associated with growth. In contrast to previous studies, we find support for Michels' iron law and conclude that peer production entails oligarchic organizational forms.