This paper studies peer effects on student achievement among first graders randomly assigned to classrooms in Tennessee’s Project STAR. The analysis uses previously unexploited pre-assignment achievement measures available for 60 percent of students. Data are not missing at random, making identification challenging. The paper develops new ways, given random assignment of individuals to classes, to identify peer effects without imposing other missing-data assumptions. Estimates suggest positive effects of mean peer lagged achievement on average. Allowing heterogeneous effects, evidence suggests lower-achieving students benefit more than higher-achieving students do from increases in peer mean. Further, the bias in a widely used, poorly understood peer-effects estimator is analyzed, implying that caution is warranted in interpreting many peer-effects estimates extant in the literature.