Apparatus for engaging and holding a non-oriented hot glass container of predetermined square cross sectional contour and closed end that includes a chuck having an open end for receiving the container and an internal valve plate for abutment with the end of the container received in the chuck. The chuck is coupled to a cam-operated arm for lowering the chuck over a container. A transition plate has a square opening contoured to be closely received over the square cross section of the container, and is mounted for free rotation adjacent to the open end of the chuck. Guide fingers project from the plate away from the open end of the chuck so as to engage the container end as the chuck is lowered over the container, and to rotate the plate relative to the chuck so that the plate opening is aligned with the square cross section of the container end. A vacuum is applied to the valve plate within the chuck for holding the container end against the valve plate. Close fit between the transition plate opening and the square cross section of the container restricts flow of air through the opening past the container, and thereby improves the ability to retain and hold the container within the chuck.