Every Internet source I’ve looked at says that the word simply means ‘somebody from Mexico City.’ It’s a uniquely Mexican word; I’ve never heard a Central or South American person use it. However, the vast majority of Mexicans that I have known and worked with during the past 20 years are from the Jalisco area, and almost all of them agree that the word has a vague derogatory connotation. Some have told me that it’s simply synonymous with ‘thief,’ while others have said that it has a subtler meaning, and implies that the person to whom it is directed has a somewhat shifty, unreliable character—not necessarily somebody who has a criminal personality, but more like the type of person who doesn’t quite pull his fair share of the weight and will do as little work as he can get away with. Does the word have different meanings in separate geographical regions of Mexico?
Here in the Yucatan it identifies someone from the state of Mexico, or D.F. Nothing derogatory. In fact, people are proud to say they are chilangos.
According to the Diccionario, what it means is “1. from Mexico; 2. from Mexico City and its DF”.
At a WAG, it’s a matter of this tradition many countries have, where people from the capital consider everybody else a country bumpkin and have problems believing that a large amount of the country doesn’t want to live in the capital, whereas the provincials think that people from or living in the capital are all a bunch of lazy thieves (lazy: can’t go 500m without taking a bus; thief: have you seen how many politicians and bankers live there? And government workers who can’t get fired no matter what!). Not everybody and all that - but there are people in this world who seem to enjoy coming up with ways to look down on everybody else, and if the only reason they can find is where you’re from then they’ll use that.
In countries with additional cultural poles (such as Mexico’s own Puebla and Monterrey), there are similar issues between those and the rest. Does poblano have any implications per se? No, but I’ve heard people say “he is poblano” in tones that made this completely-factual information an insult of the “you don’t repeat that in the street” levels. Was it really meant to be an insult to all poblanos? No… just to that one, but the speaker couldn’t come up with anything else really.
There is a hostile expression in Mexico, “Haz patria, mata a un chilango” (Something like Be a patriot, kill a Mexico City person), on graffiti. This stems from the tensions Nava identified, as well as the fact that in the 1990s there was an out-migration of Chilangos to other cities in central Mexico - not unlike that from Southern California to the rest of the west. Chilangos are perceived as arrogant toward “provincials.”
My step mother is chilanga, (as well as one of my exes), and I’ve heard the term used in various ways, both in Mexico and throughout southern California–especially in Los Angeles. It’s basically what Nava said above. The connotation of any regional appellation, in any language, can vary a lot depending on who’s speaking, and what their point of view is. It’s similar in Colombia between the cachacos and the curramberos.