The Chicago Dog/Chicago Style Hot Dog is a thing of beauty, friends. It is The hot dog -- everything else in comparison is just a wiener in a bun.
The origin of the one true dog is debated, but is generally credited to Austria-Hungarian Anton Ludwig Feuchtwanger who was assembling them as early as 1893 for the Chicago Worlds Fair.
The Chicago Dog is important because, unlike traditional (term used loosely) dogs where there is too much bun and not enough other, the Chicago Dog gives an excellent overall balance -- the wiener is not the focal point of the dog, but is taken as part of the whole work of art.
The reason for this is that there is more to them than meat, bread and condiments. Individual preferences and recipes will always have some wiggle room, but generally a Chicago Dog will have steamed or boiled frank with yellow mustard, pickle relish, chopped onion, tomato wedges (not slices, wedges), a kosher dill spear and celery salt/celery seed. Acceptable (and recommended) additions are hot "sport" peppers (whole, not sliced), and some people say diced green pepper is good, though I don't prefer it myself.
There are few mandates about its assembly save a few points: the mustard will be drizzled off the side of the wiener (not on top of it), the tomato (WEDGES!) will be placed on the frank/bun crevice on one side and the pickle spear on the other. This pickle/tomato placement them builds up the sides of the 'dog and makes a neat furrow for the relish/onions/peppers to sit in without falling out before you partake.
Never put ketchup/catsup/catchup/whatever on it. Ever. It's just not an option. Deal with it.
Common hot dogs are small dishes. You need to eat at least 3 to feel them in your belly -- a Chicago Dog, on the other hand, is a complete meal because you've got more then just the bread and meat there.
The purists will tell you the wiener needs to be a Vienna Beef wiener. This is because the Vienna Beef frank was what was used in the first Chicago Style Dogs in 1893. While they are good, generally you'll be a allowed to slip by with any well-made all beef frank.. I prefer Hebrew National myself.