Unlike the DMV in the US, the Servicio de Registro Civil e Identificación really has stepped up…read moretheir game. Although you still can't make an appointment online, they have created a super efficient system to get your identity cards (even for us foreigners)!
I recommend getting there at the end of the day on a Friday - it is almost always empty. Every time I have been, the wait was 5 minutes (unlike how it used to be, when you would have to plan your day around this event because it would take a minimum of 2 hours). I have attached a picture of the line (or better, lack there of) on a Friday around 12pm.
Remember, just like any government run office, the Registro Civil closes at 2pm.
What is really convenient about this location is that it is surrounded by photocopy places and places to take pictures (just in case you forgot to do any of it before arriving).
They also have several information points if you are unsure of where you should be going and the workers are always super helpful in directing you to the appropriate line and floor depending on your "tramite" and what documents you should have present.
Also, if you have to pay for your new ID card bring cash! It also takes longer for foreigners to get their IDs than Chileans.
Just remember, to brush a comb through your hair and smile with your mouth closed for the photos (no "mean muggin' it" as these photos are very unforgiving)!
Tip:
Even though they will tell you your ID card will be ready in 1 month, I would come back after 2 weeks to check. It is usually ready by then.
You can also call if you have any questions so you don't have to make the trip.