Chilango is a Mexican slang term used to refer to a person from Mexico City, or as an adjective to refer to something from Mexico City. It may be considered pejorative when used by people from outside of Mexico City.
A more neutral term to denote a person from Mexico City is "capitalino."
There is a monthly magazine called Chilango that covers current events in Mexico City.
Who Uses the Term Chilango
In other parts of Mexico, especially the northern states, the term chilango is definitely not considered a compliment.
For some, the word only refers to a person who was born and raised in Mexico's capital, but not everyone makes that distinction. There's supposedly a chilango accent which distinguishes a person from Mexico City.
There are other terms to refer to residents of Mexico City that are less problematic. One is "defeno," which is a coined word that comes from the initials of the official Spanish name of the city, Distrito Federal (DF).
And the term "capitalino" while not exactly a compliment, is considered mostly neutral, and can refer to someone from a suburb of Mexico City rather than the city itself. If someone from another state within Mexico calls a resident of Mexico City a capitalino, it's usually intended as a put-down.
Among residents of Mexico City, the term chilango is used affectionately, and there's even the concept of "chilangolandia," or a chilango home state. In America, chilango is sometimes used to refer to a style of cuisine from Mexico City.
And there's the Chilango bus service, which travels between the U.S. and Mexico
Origins of the Term Chilango
There's some debate about the origins of the term chilango. One theory is that the word is a derivative of the Mayan word "xilan," which refers to someone with a bald head or frizzy hair. Another suggestion is that the chilango comes from the word "chilanco" in the Nahuatl language.
This translates literally to "the red ones," or red-skinned, and was how the Nahua referred to the Aztec people.
When to Avoid Using 'Chilango'
If you are not from Mexico City and don't live there (or in a nearby suburb), your best bet is to avoid using this term. While residents of the city may use it proudly, there's not much leeway for outsiders (especially Americans) to use the term in a way that's not offensive.