This 35mm screening is part of the BFI's 'Ride Lonesome: The Psychological Western' season. You can find full details here. This film is also being shown on May 13th.
Chicago Reader review:
An uncharacteristically nasty James Stewart plays an obsessive bounty hunter with Robert Ryan in tow in one of the very best Anthony Mann westerns—which means one of the very best westerns, period. This 1953 film has Janet Leigh in jeans, beautiful location shooting (and Technicolor cinematography) in the Rockies, and some of the most intense psychological warfare to be found in Mann's angular and anguished oeuvre. With Ralph Meeker, Millard Mitchell, and a top-notch script by Sam Rolfe and Harold Jack Bloom.
Here (and above) is the trailer.