After Spring’14 release users can now send Chatter messages to other members within a community. These messages allow you to have secure private chats with other users, and they don’t appear in your feed, your profile, global search results, or any other part of Chatter that’s publicly visible.
Enable Private Messages in Communities
Administrators can enable Chatter messages in individual communities n Miscellaneous settings. To enable this feature follow the below instruction
1) Click on Name | App Setup | Customize | Communities | Manage Communities | Edit next to the community name
2) Click on Miscellaneous
3) Enable Chatter messages (which allow you to have secure private conversations with other Chatter users. To expose Chatter messages for external users, administrators must also enable the Chatter tab)
4. Click Save
To Send Private Message
Follow the below instruction to send private message to other users within Communities
1) Click on the Messages link on the Chatter tab, and then click on New Message
2) Or by selecting Send a message when hovering over a member’s name, picture or available on users profile page, Same as below screen shot
Conversation can involve just one other person, or up to 10 people total, including yourself. Conversation participants are established when someone sends the first message in the conversation. No one can add people or remove people from the Conversation after the first message is sent. You can manage your email notifications for private messages in Email Settings.
Note:- Within the Salesforce user interface, a user must log in to a community to initiate a Chatter message to another member of that community.
In the list of Chatter messages, users can see private messages they have sent or received in their internal organization and any communities that they’re a member of.