Resting-state fMRI studies have revealed that individuals exhibit stable, functionally meaningful divergences in large-scale network organization. The locations with strongest deviations (called network “variants”) have a characteristic spatial distribution, with qualitative evidence from prior reports suggesting that this distribution differs across hemispheres. Hemispheric asymmetries can inform us on constraints guiding the development of these idiosyncratic regions. Here, we used data from the Human Connectome Project to systematically investigate hemispheric differences in network variants. Variants were significantly larger in the right hemisphere, particularly along the frontal operculum and medial frontal cortex. Variants in the left hemisphere appeared most commonly around the TPJ. We investigated how variant asymmetries vary by functional network and how they compare with typical network distributions. For some networks, variants seemingly increase group-average network asymmetries (e.g., the group-average language network is slightly bigger in the left hemisphere and variants also appeared more frequently in that hemisphere). For other networks, variants counter the group-average network asymmetries (e.g., the default mode network is slightly bigger in the left hemisphere, but variants were more frequent in the right hemisphere). Intriguingly, left- and right-handers differed in their network variant asymmetries for the cingulo-opercular and frontoparietal networks, suggesting that variant asymmetries are connected to lateralized traits. These findings demonstrate that idiosyncratic aspects of brain organization differ systematically across the hemispheres. We discuss how these asymmetries in brain organization may inform us on developmental constraints of network variants and how they may relate to functions differentially linked to the two hemispheres.