Gene and Jude's has my favorite in the city, although Chickie's (known mostly for their beef) on 2839 S. Pulaski has solid Vienna beef wieners with natural casing (a must for a proper Chicago hot dog.) Both of these places are the minimalist style (onions, mustard, relish, optional sport pepper) of Chicago hot dog, not the drag-through-the-garden style on a poppy seed roll.
And Portillo's, despite it being a local chain, does a solid job with the dogs, too, more of the stereotypical "Chicago dog." (The only difference, I think, is they don't use the neon relish.) The char dog at the infamous Wiener Circle is one of my favorites, too. Just don't go there on a weekend night when the drunken frat ******bag crowd comes out.