Brain vasculature is a complex and heterogeneous physiological structure that serves specialized roles in maintaining brain health and homeostasis. There is substantial interest in developing representative human models of the brain vasculature for drug screening and disease modeling applications. Many contemporary strategies have focused on culturing neurovascular cell types in hydrogels and microdevices, but it remains challenging to achieve anatomically relevant vascular structures that have physiologically similar function to their in vivo counterparts. Here, we present a strategy for isolating microvessels from cryopreserved human cortical tissue and culturing these vessels in a biomimetic gelatin-based hydrogel contained in a microfluidic device. We provide histological evidence of arteriole and capillary architectures within hydrogels, as well as anastomosis to the hydrogel edges allowing lumen perfusion. In capillaries, we demonstrate restricted diffusion of a 10 kDa dextran, indicating intact passive blood-brain barrier function. We anticipate this bona fide human brain vasculature-on-a-chip will be useful for various biotechnology applications.