Engrafting organoids into vascularized tissues in model animals, such as the immunodeficient mouse or chick embryo chorioallantoic membrane (CAM), has proven efficient for neovascularization modeling. The CAM is a richly vascularized extraembryonic membrane, which shows limited immunoreactivity, thus becoming an excellent hosting model for human origin cell transplants. This paper describes the strategy to engraft human brain organoids differentiated at multiple maturation stages into the CAM. The cellular composition of brain organoids changes with time, reflecting the milestones of human brain development. We grafted brain organoids at relevant maturation stages: neuroepithelial expansion (18 DIV), early neurogenesis (60 DIV), and early gliogenesis (180 DIV) into the CAM of embryonic day (E)7 chicken embryos. Engrafted brain organoids were harvested 5 days later and their histological features were analyzed. No histological signs of neovascularization in the grafted organoids or abnormal blood vessels adjacent to the graftings were detected. Moreover, remarkable changes were observed in the cellular composition of the grafted organoids, namely, an increase in the number of glial fibrillary acidic protein-positive-reactive astrocytes. However, the cytoarchitectural changes were dependent on the organoid maturation stage. Altogether, these results suggest that brain organoids can grow in the CAM, and they show differences in the cytoarchitecture depending on their maturation stage at grafting.