This chair belongs to the Eames Aluminum Group series which is a line of furniture designed by Charles and Ray Eames. While the furniture, particularly the task chair, is an icon of office furniture, it was originally commissioned as outdoor seating for the home of J. Irwin Miller (founder of Cummins Engines) by Eero Saarinen and Alexander Girard. The original design featured a woven supsension back and seat stretched between aluminum ribs.
The chair has been in production since its inception in 1958, although the seat material has changed over time. The original version was a gorgeous and practical mesh version, which is the one you can see here in its High Back version.