Firefox OK, but Chrome says "Not secure"

Nope, was stil there. Hitting F12 and looking in the Console section showed the problem: The page had a form to search through Google.

Removing that section fixed it.

Mixed Content: The page at 'https://www.acme.com/' was loaded over a secure connection, but contains a form that targets an insecure endpoint 'Google'. This endpoint should be made available over a secure connection.