What kind of creature is Chiyo-chichi?
According to the Azumanga Daioh wiki (revision permalink),


  Chiyo-chichi ("Chiyo-Dad" 「ちよ父」"Chiyo-chichi"), is a strange yellow cat like creature...


According to Wikipedia (revision permalink),


  "Chiyo-Father" (「ちよ父」 "Chiyo-chichi") is a strange-looking and even stranger-acting cat-like creature...


According to TVTropes, Chiyo's father is one example of a Mega Neko or is a Mind Screw element that was added to the anime by the author to keep the audience guessing. About who or what he really is, only Azuma knows.