We consider the case in which the number of seats in a program is limited, such as a job training program or a supplemental tutoring program, and explore the implications that peer effects have for which individuals should be assigned to the limited seats. In the frequently-studied case in which all applicants are assigned to a group, the average outcome is not changed by shuffling the group assignments if the peer effect is linear in the average composition of peers. However, when there are fewer seats than applicants, the presence of linear-in-means peer effects can dramatically influence the optimal choice of who gets to participate. We illustrate how peer effects impact optimal seat assignment, both under a general social welfare function and under two commonly used social welfare functions. We next use data from a recent job training RCT to provide the first evidence of large peer effects in the context of job training for disadvantaged adults. Finally, we combine the two results to show that the program's effectiveness varies greatly depending on whether the assignment choices account for or ignore peer effects.