Totally forgot I made this thread, probably because I've suppressed every post I made in 2016/2017 from my memory.

I personally define "rarity" as being a species that's found in five or less holders in the country. Here are some species held at the Chicago collections that meet that criteria:
Brookfield Zoo Chicago
Black and Rufous Sengi (one of four holders in the US)
Crested Capuchin (one of three holders outside of the South America)
Small-spotted Genet (no more than a handful of other AZA holders)
Southern Hairy-nosed Wombat (One of five holders in the US)
White-bellied Pangolin (one of only two holders worldwide, only public exhibitor).
Greater Prairie-Chicken (only public exhibitor in the country, only known holder of the
pinnatus subspecies)
Lincoln Park Zoo
Bourke's Parrot (One of five holders in the US)
Green Broadbill (one of three holders worldwide)
Kagu (one of five holders in the US)
Puerto Rican Parrot (only holder outside of Puerto Rico)