As political polarization in the United States continues to rise, the question of whether polarized individuals can fruitfully cooperate becomes pressing. Although diversity of individual perspectives typically leads to superior team performance on complex tasks, strong political perspectives have been associated with conflict, misinformation and a reluctance to engage with people and perspectives beyond one's echo chamber. It is unclear whether self-selected teams of politically diverse individuals will create higher or lower quality outcomes. In this paper, we explore the effect of team political composition on performance through analysis of millions of edits to Wikipedia's Political, Social Issues, and Science articles. We measure editors' political alignments by their contributions to conservative versus liberal articles. A survey of editors validates that those who primarily edit liberal articles identify more strongly with the Democratic party and those who edit conservative ones with the Republican party. Our analysis then reveals that polarized teams---those consisting of a balanced set of politically diverse editors---create articles of higher quality than politically homogeneous teams. The effect appears most strongly in Wikipedia's Political articles, but is also observed in Social Issues and even Science articles. Analysis of article "talk pages" reveals that politically polarized teams engage in longer, more constructive, competitive, and substantively focused but linguistically diverse debates than political moderates. More intense use of Wikipedia policies by politically diverse teams suggests institutional design principles to help unleash the power of politically polarized teams.