Needs to be fully self hostable and open source.
If you want security, run Zulip behind a firewall.
We tested a whole bunch of chat systems, and found that Zulip was the most user-friendly for less-technical people, while still having a non-annoying interface for technical folks who would have been happy with XMPP.
The only negative we've seen in Zulip is the tendency for people to occasionally respond in the last topic that they read rather than the one they meant to -- but that can be fixed by users or admins, so it's only slightly annoying now.