Currently looking into this myself. A few observations:
1.) Grades don't really matter. You'll want to graduate with some distinction, but other than that, cum laude vs. magna vs. coif vs. summa isn't super important. BUT...
2.) For some fields -- con law, federal courts, civ pro, etc. -- a COA or USSC clerkship is really important. And obviously you need great grades for that. But outside of those fields, it's not such a big deal. I guess I'd put it this way: If you really wanted to teach property or bankruptcy or trusts, a law degree from HSYCh plus a published article plus a few years work experience in the relevant field would open up a LOT of doors.
3.) Speaking of HSYCh, as someone above noted, the academic feeder pecking order goes Yale -> big, huge dropoff -> Harvard -> imperceptible dropoff -> Stanford and Chicago (tie) -> big huge dropoff -> Columbia -> big, huge, massive dropoff -> NYU, Michigan, Boalt, Virginia. Some people even claim that the smaller class sizes and increased opportunity for faculty interaction at Stanford and (especially) Chicago make them preferable to Harvard.
4.) A JD is not strictly necessary, depending on the field. You may well have luck on the market with "only" a PhD.
5.) Speaking of work experience, 5 years is kind of the cutoff. More than that and it starts to count against you. BUT...
6.) This isn't true in some areas -- corporate law, property, tax, etc. And you can always wash away the "stain" of being out too long by publishing.
7.) Speaking of publishing, you're not going to get a sniff by law schools if you don't have an article placed in a top 100 law review. (Exceptions: If you are a Supreme Court clerk, or if you are in one of a few more specialized fields and have an article placed in one of the corresponding specialized journals.) Even then, you'll probably need a second one to be really successful.
8.) If you limit yourself to Chicago schools, the chances of getting a job are miniscule.
9.) That said, if you did get a U of C JD to go along with your PhD, you might look into a Visiting Assistant Professorship or a fellowship. Northwestern and Chicago-Kent both have good programs along the former lines, and Chicago's Bigelow program is, of course, notorious for placing alums really, really well.