The Mangosteen & Durian website says the mangosteen is rare outside Southeast Asia and keeps only a few days without refrigeration. However, storage at 10*C "extends shelf life to about 20 days". In other words, this fruit is not a great keeper so may not travel well. If it is anywhere in Chicago I would expect it to be in the produce departments of Viet Namese grocery stores on Argyle Street or on Sheridan or Broadway near Argyle. In case it's seasonal you might ask at the stores about mangosteen's ETA.
>>You mean mangosteen chewing gum from Japan????!!!!!<<
I don't think so. I think they mean a specific fruit found in SE Asia. It's purplish in color, like an eggplant, as small as an tangerine, with a thick rind much like the texture of egg carton cardboard. The fruit is white, more sweet than sour, and encompasses a smooth brown pit. Also, like a citrus fruit, the fruit comes apart in segments. They're delectable and I adore them.
I've had the opportunity to sample them on various trips to Asia and have discovered they're not available year-round. According to the people I've asked, they seem to be in season largely in the early summer.