SARS-CoV-2 has undergone repeated and rapid evolution to circumvent host immunity. However, outside of prolonged infections in immunocompromised hosts, within-host positive selection has rarely been detected. Here we combine daily longitudinal sampling of individuals with replicate sequencing to increase the accuracy of and lower the threshold for variant calling. We sequenced 577 specimens from 105 individuals in a household cohort during the BA.1/BA.2 variant period. Individuals exhibited extremely low viral diversity, and we estimated a low within-host evolutionary rate. Within-host dynamics were dominated by genetic drift and purifying selection. Positive selection was rare but highly concentrated in spike. A Wright Fisher Approximate Bayesian Computational model identified positive selection at 14 loci with 7 in spike, including S:448 and S:339. This detectable immune-mediated selection is unusual in acute respiratory infections and may be caused by the relatively narrow antibody repertoire in individuals during the early Omicron phase of the SARS-CoV-2 pandemic.