LAN Chat via OS X Server — Will Messages App Suffice?
You have a couple of options using native Apple tools:

Apple's iMessage service utilizes free iCloud accounts. The service works with the Messages app (both on Mountain Lion &amp; iOS). All messages are routed through Apple's servers. Certificate-based encryption is used, but Apple does not document its exact nature or whether the messages get unencrypted on their servers. Here are some resources that might be helpful for looking more into this option:


IMFreedom
iCloud Security


OS X Server also has a Messages service that can be turned on. This creates an in-house messaging service based on the Jabber/XMPP protocol. It is by definition secure, as it routes through your in-house server. It works natively with Messages and/or iChat on the Mac (depending on OS X version) and works with a variety of apps available on the App Store. This is the way to go if you are seriously concerned about security of your conversations.