I always thought it was the El, but then again I've never been to Chicago. So take from that what you will.

Well, it's an abbreviation for "elevated", so...it could be either. But knowing what it means might help you decide what works best for you? Personally, I choose to never put it in writing, so I can avoid having to decide which is correct. If I had to, I'd go with the shorter of the two, obviously - "L".

in another thread an actual Chicagoan is calling it the "eL". Which seems a little awkward at first, but sort of grows on you.

According to the CTA:

CTA’s train system is called the ‘L’, short for "elevated."

sort of either, sort of not.

but I should also say, it's never "eL."