Perceived stress, which refers to people's evaluation of a stressful event and their ability to cope with it, has emerged as a stable predictor for physical and mental health outcomes. Increasing evidence has suggested the buffering effect of social support on perceived stress. Although previous studies have investigated the brain structural features (e.g., gray matter volume) associated with perceived stress, less is known about the association between perceived chronic stress and intra-cortical myelin (ICM), which is an important microstructure of brain and is essential for healthy brain functions, and the role of social support in this association. Using a sample of 1076 healthy young adults drawn from the Human Connectome Project, we quantified the ICMby the contrast of T1w and T2w images and examined its association with perceived chronic stress during the last month and social support. Behavioral results showed that perceived chronic stress was negatively associated with both emotional support and instrumental support. Vertex-wise multiple regression analyses revealed that higher level of perceived chronic stress was significantly associated with lower ICM content of a cluster in the right supramarginal gyrus (rSMG). Interestingly, the emotional support, but not the instrumental support, significantly mediated the association of perceived chronic stress with ICM in the rSMG. Overall, the present study provides novel evidence for the cortical myelination of perceived chronic stress in humans and highlights the essential role of the rSMG in perceived chronic stress and emotional support.