I don't know but I'd sure like to help design one!
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The chair I'm thinking of is called the "Ball" or "Globe." It was designed by Eero Aarnio, a designer from Finland. Made from moulded fibreglass-reinforced polyester seating section on painted aluminum base with internal fabric-covered foam upholstery. Circa 1966 - 1980 very retro!!
Try Ebay under "retro" or "mid-century modern design," or your local 2nd hand vintage store. They are very rare and will be in the thousands of dollars for an original.
They may still be in production but probably without the built-in stereo - very cool!