Many supporters of political reform advocate opening party nominations to non-members as a way of increasing the number of moderate elected officials. This presumes that the composition of the primary electorate is, in fact, a significant cause of polarization, an idea that has rarely been tested empirically. We marry a unique new data set of state legislator ideal points to a detailed accounting of primary systems to gauge the effect of primary systems on polarization. The results of this analysis suggest that the openness of a primary election has little effect, if any, on the partisanship of the politicians it produces. We speculate on why the effect is so inconsistent and weak, and discuss the implications of our study for the theoretical literature on parties in American political life.