Although law schools are increasingly hiring faculty without requiring visiting stints first, a handful of the very top law schools still have sufficient appeal and market clout to require those visits in almost all instances. Now that law school website are updated, here are the visiting faculty at Yale, Harvard, Stanford, and Chicago for this academic year:
Yale Law School requires all those designated as "visiting professors" to pass through a vote of the full faculty, meaning that all those so designated are, to some degree, being considered for permanent appointment (though, in practice, the degree differs). (This is also why at YLS one will sometimes see well-known senior academics at other law schools listed as "lecturers" when teaching a term at Yale--they haven't been through the official process). Putting aside two senior foreign academics who are probably not going to move permanently and who have visited previously at Yale--namely, Dieter Grimm from Germany and Michael Trebilcock from Canada--the academic visitors under some degree of consideration are: Lee Anne Fennell (behavioral law & economics) from the University of Illinois; Heather Gerken (voting rights) from Harvard; Douglas Kysar (behavioral law & economics) from Cornell; Tracey Meares (criminal law) from University of Chicago; Eduardo M. Peñalver (property, land use) from Fordham; Lawrence M. Solan (law & linguistics, statutory interpretation) from Brooklyn Law School; George Triantis (law & economics, corporate) from the University of Virginia; and Eric Zolt (tax) from UCLA.
Harvard Law School, unlike Yale, has a huge number of visitors each year, many of whom are filling curricular needs, and are not being considered for appointment (this is often true of those visiting from Boston-area schools). From the outside, it's hard to know with certainty who is a "look-see" visitor (i.e., under active consideration for appointment) and who is not. I know my colleague Philip Bobbitt (constitutional law, national security law and policy) is in the former category, and I strongly suspect the legal historians Mary Dudziak (Southern California) and Michael Klarman (Virginia) are too--but I would also guess a dozen others among this year's visiting professors are under some degree of consideration for permanent appointment.
Stanford Law School is more like Yale in having relatively few visitors, though they have, historically, hired permanently hardly any of those who have visited. (Like Harvard, they also seem to have a small number of Bay Area "podium" visitors, i.e., those filling a curricular need.) My guess from the outside would be that Stanford is quite interested in several of these folks, but, as with past practice, they are unlikely to hire more than one or two of them, if that. The Stanford visitors are: Christopher Kutz (criminal, law & philosophy) from Berkeley; David Luban (legal ethics) from Georgetown; Nathaniel Persily (voting right, election law) from Penn; Jane Schachter (legislation, statutory interpretation) from Wisconsin; Alan Sykes (international law and trade) from University of Chicago; and Timothy Wu (intellectual property) from Columbia. (Perhaps, under a new Dean, Larry Kramer, their hiring practices are about to change.)
University of Chicago Law School is, again, closer to the Yale model than the Harvard model on visitors, though like Yale and Stanford, they have hired permanently only a minority of the visitors (choose "visiting faculty" in the search engine to see the list). Putting aside the foreign visitors (some of them repeat visitors to Chicago), the visiting academic faculty are Michael Abramowicz (corporate, civil procedure, law & econ) from George Washington University; Stephanos Bibas (criminal law & procedure) from the University of Iowa; Eugene Kontorovich (public law, law & economics) from George Mason University; Anup Malani (health law, corporate law, law & economics) from the University of Virginia; Richard McAdams (criminal law, law & social norms) from the University of Illinois; and Frederick Schauer (constitutional law, jurisprudence) from Harvard's Kennedy School, whom Chicago has tried to recruit off and on for many years. (Schauer will almost certainly not move permanently to Chicago.)
When time permits, I'll update this listing with info on Columbia and NYU as well.