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

Yes. Because of daylight saving time the gap moves between +12h and +13h.

When is the best time to call Chicago from Bangkok?

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

Bangkok is 12h ahead of Chicago. This gap is not fixed: daylight saving time moves it between +12h and +13h during the year.

Bangkok

Thailand

--:--:--

Chicago

United States

--:--:--

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

City	Time zone	UTC offset
Bangkok · Thailand	Asia/Bangkok	UTC+7
Chicago · United States	America/Chicago	UTC−5

What is the time difference between Bangkok and Chicago?: Bangkok is 12h ahead of Chicago. This gap is not fixed: daylight saving time moves it between +12h and +13h during the year.
Does the time difference between Bangkok and Chicago change during the year?: Yes. Because of daylight saving time the gap moves between +12h and +13h.
When is the best time to call Chicago from Bangkok?: There is no overlap between standard working days, so one side has to call early or late.