Why does New York have subways, but Chicago has elevated trains?

Underground train lines are 10 times more costly to build, and 3 times more costly to maintain than level or elevated train lines.

Orthodoxy = the only true faith; Roman Catholics tried one cup - one spoon ritual and got sick with Bubonic plague; if heresy enters Orthodox monastery then monks/nuns will get sick with flu/tuberculosis (for instance); Orthodox churches who closed for COVID or had disposable cups/spoons or dipped spoon into alcohol are no longer brides of Christ (now they serve Satan and honor Satan's new COVID religion). Priests who were working for KGB (that is spying on people and betraying their confession) = Sergian heresy. Now, CIA and FSB (new name for KGB) don't need to have priests constantly reporting because of new technology (bugs) that allows them to listen in (and if cameras are present... to look into what people are doing)...Your phones spy on you; don't bring them to church; forgive me.

I think the primary reason is how developed the city was. Chicago had a fire in 1871 and was rebuilt in a large portion. This allowed and encouraged a cheaper (as well as quicker) way to build a mass transit system.

The "L" was started in 1892 and steam locomotives were used, coal fired locomotives make operation in subways very unhealthy.

The "subway system" started operation in 1904 and was a replacement for the street car system. The object was to remove the mass transit system to where it did not interfere with street traffic. By this time electrified motive power and of course electricity to be developed to a point it was feasible. Keep in mind the supporting structure for the track would take away space at street level.

Having been on the subway system of NYC, I can tell you much of it is elevated. But in the areas which have been developed for a long time it is underground because there just isn't room for everything at street level. There is also by the way a large rail system for freight underground and tunnels that are used for utilities including steam lines that are  used to provide heat to other buildings.

It would be interesting some time to study more of what is underground in NYC and see how much takes place below ground that very few even knows happens.

The NYC subway system is only underground in certain areas, mostly Manhattan. There’s no room for elevated trains in Manhattan. The other boroughs have elevated trains just like Chicago. 

The New York "subway" is only underground in some places; it is elevated in some places.

Well, because Chicago had  plenty of space to build above ground which is a lot less costly than building underground.  Also Chicago has a low water table, being build on low ground that was often swampy, and pumping a lot of water out of tunnels and making them last is more costly.