While Zimbra recommends the admin GUI, I have not been able to get this right. I just use the command line. I don't know who your CA provider is but Zimbra plays by different rules when it comes to this. I found this link very helpful
5.x Commercial Certificates Guide - Zimbra :: Wiki
NOTE: This is tailored to Version 5 but it worked in Version 6
If you decide to use the GUI, one problem you may observe is that after applying the certificate, Zimbra fails when starting the mail box. This URL is not directly related but it fixed my broken certificate allowing other things to work right.
ZCS Network Install: Was working, now possibly broken due to SSL?
Good Luck