Why people get chills after drinking cold beverages?

Body needs balance. If you feel cold or have chills after drinking a cold beverage, then your body is responding to this environmental change and making you 'feel' something so that the balance can be restored. For example, if you feel too cold, you will stop drinking that cold beverage - or take other steps to balance that out. Such as put on a light jacket. Europeans don't generally put ice in their drinks, BTW.