The high selectivity of the human blood-brain barrier (BBB) restricts delivery of many pharmaceuticals and therapeutic antibodies to the central nervous system. Here, we describe an in vitro microfluidic organ-on-a-chip BBB model lined by induced pluripotent stem cell-derived human brain microvascular endothelium interfaced with primary human brain astrocytes and pericytes that recapitulates the high level of barrier function of the in vivo human BBB for at least one week in culture. The endothelium expresses high levels of tight junction proteins and functional efflux pumps, and it displays selective transcytosis of peptides and antibodies previously observed in vivo. Increased barrier functionality was accomplished using a developmentally-inspired induction protocol that includes a period of differentiation under hypoxic conditions. This enhanced BBB Chip may therefore represent a new in vitro tool for development and validation of delivery systems that transport drugs and therapeutic antibodies across the human BBB.