Y'know, Chibi art and Anime art come hand-in-hand. This is because some anime, be it Saturday morning or high-comedy prime-time, tend to use "Deforms" to exaggerate the expressions of the characters. Good examples are Blaz-blue, Full-Metal Alchemist, Tri-gun, Pokemon, Ninja Soul, and other shows/games/manga.
There is a distinction, I'm not arguing that. But when you said "I've never seen an anime look like chibi" I wonder how much anime you've seen: how could you miss the near regular presentation of chibi art in most shows?