This article covers 

Why can’t I see the “Clear Personal Data” button on the Customers tab
Clear Personal Data button not shown on the Customers page to delete PII data

Summary

PII for a customer record can be deleted when and only when all subscriptions associated with the record are in a cancelled state. Once deleted, the data cannot be recovered by any means so please observe caution, especially when setting the data retention period field to "immediately".

You can use the web interface to issue deletion requests for individual customer records. This is done using the Clear Personal Data button on the customer details page. The button is only shown for eligible customer records.

Solution 
Pre-requisites:
1. List of Personal Data is configured under Settings > Configure Chargebee > Personal Data.
2. All subscriptions associated with the record are in cancelled state.

Answer:
Only the "Admin" role (with Full Access) will have access to the "Clear Personal Data" button for the Customers as per the Personal Data Management governance in Chargebee for PII data.

The below user roles will not have access to this action by design:

1. Tech Support

2. Analyst

3, Sales Agent

4. Customer Support

5. Sales Manager

6. Finance Executive

Once this action is performed, there is no way to recover the lost information as per the GDPR compliance requirements.

It is possible to create custom roles in your Chargebee site that include the permission to clear PII data.  You can read more about custom roles here

Related articles and Documentation
https://www.chargebee.com/docs/2.0/personal-data-management.html
https://www.chargebee.com/docs/2.0/personal-data-management.html#faq