|Your new browser looking out for your best interests.|
Google has decided to be rather unforgiving (maybe call it condescending?) and not even provide an interactive way for a Chrome user to opt out of their security measures.
The real fix is to upgrade / patch your systems to versions that rectify the vulnerabilities.
In the interim, there are workarounds for most browsers if you care to suggest your users go that route.
For Firefox (the one I use):
Navigate to about:config in the address bar.
Choose “I’ll be careful”
Search for security.ssl3.dhe_rsa_aes
Double click security.ssl3.dhe_rsa_aes_128_sha and security.ssl3.dhe_rsa_aes_256_sha to change them to false.
For Chrome (I haven’t tried this personally but is the commonly referenced workaround):
In MS Windows, right click on desktop and choose New | Shortcut
In the location field, including the double quotation marks enter "C:\Program Files (x86)\Google\Chrome\Application\chrome.exe" --cipher-suite-blacklist=0x0039,0x0033
Choose Next and enter a name like “CUCM Chrome” and Finish.
You should be able to use that shortcut to start a version of Chrome access the CUCM interface.