What kind of creature is Chiyo-chichi? Chiyo-chichi (Chiyo-Dad, or "Father Cat" in the dub) is a strange creature that appears in  Osaka and Sakaki's dreams. He says he's not a real cat before he tells Sakaki to "find a real cat."

What kind of creature is he? Where did the author get the idea of creating him?

He's the strange creature in the middle -- he doesn't like tomatoes because they are red :
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.