In the Azumanga Daioh universe, only Sakaki and Osaka seem to have the shared image of Chiyo-chichi as a yellow cat(-like creature), and he is visible to the viewer a few times. If we go by Carl Jung's definition of the extravert and introvert, (as far as I remember) the introvert is more in touch with the collective unconscious and the archetypes while the extravert is more in touch with the persona and the outside world. Since two characters that are aware of Chiyo-chichi can be considered as introverts, could Chiyo-chichi be a part of the collective unconscious? That could also explain why there exists plushies in the image of Him in the Azumanga Daioh universe.
Sounds like CBT alright