Although absenteeism has long been recognized as a threat to student achievement, its mirror image—presenteeism, attending school when one should not—has received almost no attention. This paper develops the first theoretical and empirical framework for studying school presenteeism and its consequences. I adapt the standard labor-leisure model to the school context, showing that students with highly inelastic attendance preferences—those who always attend regardless of productivity shocks such as illness—can impose negative externalities on peers through either health-related or congestive mechanisms. Using administrative data on roughly 200,000 New York City elementary school students from 2013–2019, I construct proxies for presenteeism based on students with perfect or near-perfect past attendance and estimate peer effects with a linear-in-means model that includes school-year fixed effects and instrumented lagged outcomes. Students previously achieving perfect attendance behave distinctly from nearly perfect attenders, exhibiting highly inelastic attendance patterns consistent with the model. Greater classroom exposure to these “presenteeism-prone” peers increases student absences and lowers test performance. Robustness checks restricting to randomly assigned schools and including teacher fixed effects confirm the pattern, though attenuated by sorting. The findings suggest that excessive attendance may be as detrimental to learning environments as absenteeism. Policies that exclusively reward perfect attendance, without accounting for illness or engagement, risk undermining both student health and academic productivity through unrecognized presenteeism spillovers.