After creating some more complex models/containers with threaded attachments and supports, finally came up with this simple and less bulky design.
The smaller cap goes into the larger portion. The larger part attaches to the top of the Burt's Bees' by friction with a snug fit (printed at same inside diameter of 15.72mm). The top cap then acts as a hole for the keychain and can be used with slight force to push the chapstick off of the holder. If your chapstick is a different diameter, you can likely scale the models up or down slightly to get a snug fit. The keychain hole is 3mm diameter and fits the keychain shown really well. Smaller keychain preferable if you want less bulk.
Printed at 20% infill, no supports needed. Print with flat sides down.
The author hasn't provided the model origin yet.