Chatter messages are one of the handy little features within Chatter. I'm often in a conversation in chatter with somebody when I need to make a private comment to them and don't want to go back to email or someplace outside of the system.
This is what SFDC Internal Chatter looks like for me:
Here is what Chatter looks like the community:
I can don't see any limitations in the chatter settings or in the community profiles. So I don't see why it isn't there.
Is that a feature that is not permitted in a community?
Any thoughts would be much appreciated!
Private (Direct) Messages in Chatter Communities is not a feature yet. Here is an idea you can vote on for that feature: https://success.salesforce.com/ideaView?id=08730000000kry4AAA.
Update: This feature is available as of the Spring 14 release.