Why won't my MailChimp API Key work?

When saving my new MailChimp API key, I'm receiving the following errors in the log.

[January 26, 2015 7:09 pm] [CODE:http_request_failed] [EMAIL:] - Problem with the SSL CA cert (path? access rights?)
[January 26, 2015 7:09 pm] [CODE:http_request_failed] [EMAIL:] - Problem with the SSL CA cert (path? access rights?)
[January 26, 2015 7:09 pm] [CODE:http_request_failed] [EMAIL:] - Problem with the SSL CA cert (path? access rights?)
[January 26, 2015 7:09 pm] [CODE:http_request_failed] [EMAIL:] - Problem with the SSL CA cert (path? access rights?)

What would be causing this?