Chili - generally refers to to a thick stew or soup prepared with beans and meat.
Chile - refers to peppers grown in a region.
The interesting thing about Wiki's description is that right after this declaration they list chili rellenos (stuffed chiles) spelled with an I? So the debate continues.
My organized Virgo-ness would like to have a definitive answer. But my Gemini moon loves that we can still morph the spelling to fit our ever changing minds. So my friends, the moral of the story is that there is a rule written in mud. Just enjoy your chiles, chilis! Take care of the taste buds and let an English professor worry about the spelling.
Here is Fred's awesome Chili with a chile (jalapeno) swimming in it.
Some Jalapeno Chiles growing in our garden