Zend certified PHP/Magento developer

Diagnosing server-side ERR_SSL_PROTOCOL_ERRORs

I’m copying my website’s production environment to local development, and getting “ERR_SSL_PROTOCOL_ERROR”. All the debugging advice I’m digging up assumes the website is flawless, and the problem is on the browser side.

When you’re sure the problem is on the server side, how do you get Chrome to cough up a more useful error message, to get to a solution faster?