A device and method for aseptically storing and dispensing a liquid. The device has container forming a variable-volume storage chamber, and a one-way valve coupled in fluid communication with the storage chamber and having an elastic valve member forming a normally closed valve opening. The valve member is movable between a normally closed position, and an open position with at least a segment of the elastic valve member spaced radially away from the closed position to allow the passage of fluid from the storage chamber through the valve opening. The liquid is maintained hermetically sealed in the storage chamber with respect to ambient atmosphere throughout dispensing multiple portions of the liquid from the storage chamber through the one-way valve.