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

Yes. Because of daylight saving time the gap moves between +17h and +19h.

When is the best time to call Chicago from Auckland?

Between 09:00 and 10:00 in Auckland, which is 16:00 to 17:00 in Chicago.

Auckland is 17h ahead of Chicago. This gap is not fixed: daylight saving time moves it between +17h and +19h during the year.

Auckland

New Zealand

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Chicago

United States

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A 9-to-5 day in each city overlaps for 1h. That is 09:00–10:00 in Auckland, which is 16:00–17:00 in Chicago.

City	Time zone	UTC offset
Auckland · New Zealand	Pacific/Auckland	UTC+12
Chicago · United States	America/Chicago	UTC−5

What is the time difference between Auckland and Chicago?: Auckland is 17h ahead of Chicago. This gap is not fixed: daylight saving time moves it between +17h and +19h during the year.
Does the time difference between Auckland and Chicago change during the year?: Yes. Because of daylight saving time the gap moves between +17h and +19h.
When is the best time to call Chicago from Auckland?: Between 09:00 and 10:00 in Auckland, which is 16:00 to 17:00 in Chicago.