An ink supply for an inkjet printer is provided with a main reservoir, which is typically maintained at ambient pressure. The main reservoir, which has flexible side walls supported by a rigid frame, is coupled to a variable volume chamber via a check valve which allows the flow of ink from the reservoir to the chamber and limits the flow of ink from the chamber to the reservoir. The chamber is coupled to a fluid outlet which is normally closed to prevent the flow of ink. However, when the ink supply is installed in a printer, the fluid outlet establishes a fluid connection between the chamber and the printer. The chamber is part of a pump provided with the ink supply that can be actuated to supply ink from the reservoir to the printer.