This article 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% of students. Data are not missing at random, making identification challenging. This study develops and applies new ways to identify peer effects in the presence of missing data, which incorporate knowledge of how groups form. Estimates suggest sizeable positive effects of mean peer lagged achievement on average. Analysis of a common peer-effects estimator implies caution is warranted in interpreting many peer-effect estimates extant in the literature.