A system for assembling a container and closure comprising an expanding collet which has a plurality of pivoting collet segments, each configured to simultaneously pivot radially outward about a pivot point and comprising. The collet comprises a lip that is engagable with the rim of the open end of the container and an angled tip positioned radially inward from the lip and shaped to press a countersink portion of the closure against an interior wall of the container as the collet segments pivot radially outward. As the container and the chuck are brought together, the rim engages with the lips of the collet segments and causes the angled tips of the collet segments to pivot outward toward the interior wall of the container, thereby pushing the countersink portion of the closure against the interior wall of the container.