An apparatus for storing fluid and dispensing multiple portions of the stored fluid has a container defining a variable-volume storage chamber; a dispensing valve including a valve inlet coupled in fluid communication with the variable-volume storage chamber, and an elastic valve member in fluid communication with the valve inlet and defining a normally-closed valve opening; a manually engageable actuator; and a pump including a compressible member defining a compression chamber coupled in fluid communication with the variable-volume storage chamber. Multiple portions of the stored fluid are hermetically sealed in the variable-volume storage chamber. The actuator is manually engageable and movable between (i) a first position wherein the compression chamber defines a first volume, and (ii) a second position wherein the compression chamber defines a second volume less than the first volume. In the second position the fluid in the compression chamber exceeds a valve opening pressure and, in turn, moves the elastic valve member between (i) a normally closed position hermetically sealing the one-way valve and variable-volume storage chamber with respect to ambient atmosphere, and (ii) an open position permitting fluid flow through the valve opening.