This article also answers
Why should I pass the ZIP code if my gateway doesn’t mandate it?

Solution

You would have to disable zip code validation on your Card Address verification mechanism in order to create customer via APIs without passing the zip code information.

Please navigate to Settings >> Billing Rules >>Card Address Verification >> Uncheck ZIP/Postal 

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Note:
1)  If ZIP codes are passed via API for the billing address, they'd be validated invariably. Ensure that you do not pass the ‘card[billing_zip]’parameter if you do not have the zip code information.

2) Please note that you are not required to pass the ZIP code information if the gateway doesn't mandate it. ZIP code gets always validated if it's passed via APIs, and all you need to do is follow the steps above and disable zip code validation. 



If you have any further questions regarding this, please reach out to support@chargebee.com.