A simple structure for a container closure system that allows for ease in closure and removal of a cap from the container is disclosed. The container closure comprises a cap having a skirt of substantially rectangular cross-section. Disposed in a central location on each of the internal surfaces of the skirt are rim-engaging members that are substantially coplanar. The container has a neck portion terminating in an outer peripheral rim surrounding an oval-shaped opening in one end of the container through which the container contents may be dispensed. Cap-engaging portions on the outer portion of the peripheral rim engage with the rim-engaging members disposed on the skirt internal surface when the cap is in a closed position over the container opening. The rim-engaging members of the present invention can be in the form of small ridges or grooves and can engage with cap-engaging portions formed by small ribs. Alternatively, when in the form of small ridges, rim-engaging members can engage with cap-engaging portions in the form of a small edge extending around the outer portion of the peripheral rim. The cap may be placed into a closed position on the container by aligning the edge of the skirt with a similarly configured edge of the container body and “snapping” the rim-engaging members on the skirt into an engaged relationship with the cap-engaging portions on the peripheral rim. When the cap is in a closed position, the container, its contents, and the cap can be lifted solely by gripping the cap. By twisting the cap slightly with respect to a vertical axis of the container, the rim-engaging members and the cap-engaging portions are disengaged, thereby releasing the cap to an open position so that it may be removed from the container.