Let's clear up the confusion about the spelling of chile. Here in New Mexico, chile with an 'e' refers to the pepper. It can also refer to a soup, a sauce or a stew made with green or red chiles. Now, chili with an 'i' at the end is a dish of meat and beans. Think Wolf brand chili.
Many people refer to a chile as a chile pepper. It is both a chile and a pepper, so it is ok to say chile pepper when describing a pepper with heat. The search term 'chili pepper' is searched for 5 times more often than 'chile pepper'. Why is this? It might be the same reason people think New Mexico is a foreign country.
Chiles came to the southwest from Spain in the 16th century. Along the way, some regions Americanized the Spanish word chile to become chili. Donuts, theaters, and mustaches all have been Americanized, but they are still identical items when spelled either way. The word chili was already taken and means meat and beans.
Chile with an 'e' is a New Mexican pepper and the only correct spelling according to this New Mexican. It's still ok to use chili or chilli when referring to peppers, but not here in New Mexico :)