Are you on HipChat Server or HipChat Cloud? If it's HipChat Server, I would check to make sure that the SSL certificate installed is compliant with what we have listed here: https://confluence.atlassian.com/hc/creating-or-obtaining-an-ssl-key-and-certificate-608731891.html
Otherwise, it may be beneficial to file a support ticket at support.atlassian.com and have one of the SE's take a look.
HipChat Server Support Engineer | Atlassian
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