Apparatus (10) for helping to protect an occupant of a vehicle (12) that has a side structure (16) and a roof (18) includes an inflatable vehicle occupant protection device (14) that is inflatable into a position between the side structure of the vehicle and a vehicle occupant. An inflation fluid source (24) provides inflation fluid for inflating the protection device (14). The protection device (14), when inflated, has a perimeter (44) and front and rear portions (58 and 60) spaced apart horizontally along the protection device. The protection device (14) includes overlying panels (40 and 42) that define an inflatable volume and at least one connection (80) within the perimeter (44) at which the overlying panels are interconnected. The at least one connection (80) defines inflatable chambers (100) of the protection device (14) that extend between the front and rear portions (58 and 60) in a generally horizontal direction when the protection device is inflated. The front and rear portions (58 and 60) are inflated more rapidly away from the vehicle roof (18) than the chambers (100) are inflated when the protection device (14) is inflated.