Does the time difference between Chicago and Dubai change during the year?

Yes. Because of daylight saving time the gap moves between −10h and −9h.

When is the best time to call Dubai from Chicago?

There is no overlap between standard working days, so one side has to call early or late.

Chicago is 9h behind Dubai. This gap is not fixed: daylight saving time moves it between −10h and −9h during the year.

Chicago

United States

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Dubai

United Arab Emirates

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A 9-to-5 working day in Chicago does not overlap one in Dubai at all — somebody has to take the call outside office hours.

City	Time zone	UTC offset
Chicago · United States	America/Chicago	UTC−5
Dubai · United Arab Emirates	Asia/Dubai	UTC+4

What is the time difference between Chicago and Dubai?: Chicago is 9h behind Dubai. This gap is not fixed: daylight saving time moves it between −10h and −9h during the year.
Does the time difference between Chicago and Dubai change during the year?: Yes. Because of daylight saving time the gap moves between −10h and −9h.
When is the best time to call Dubai from Chicago?: There is no overlap between standard working days, so one side has to call early or late.