Is it possible to make Customer Chat Plugin works inside an iframe ?
It's adding content-security-policy: frame-ancestors IFRAME_DOMAIN and show Refused to frame 'https://www.facebook.com/' because an ancestor violates the following Content Security Policy directive: "frame-ancestors IFRAME_DOMAIN
Yes, FB Chat Plugin is intended to be embedded.
You have just to whitelist domains where Chat allowed to operate. This should fix frame-ancestors issue in the Facebook's CSP.
And maybe you'll have to add intent: and fb-messenger: schemes.