Capital appearance in outskirts of Chicago (5)
I believe the answer is:
cairo
'capital' is the definition.
(capital of Egypt)
'appearance in outskirts of chicago' is the wordplay.
'appearance' becomes 'air' (both can mean an impression or character).
'in' is an insertion indicator.
'outskirts of' suggests removing the centre (only letters on the outskirts).
'chicago' with its middle taken out is 'co'.
'air' placed within 'co' is 'CAIRO'.
(Other definitions for cairo that I've seen before include "City near the Nile delta" , "Al Qahira" , "African city" , "Egyptian capital" , "Capital of Egypt" .)