Disable or hide all parts of Private Chat

Hello WPMU Team:

On our BuddyPress site, I'd like to disable the private chat portion of Chat. We want to try using Chat only on Group pages. I'm not finding a setting to the effect of "Allow/Disallow Private Chatting."

If that feature does not exist, I'd be fine with hiding private Chat elements with CSS code. The places to hide it are:

1. The Availability button on a member's profile.

2. The Availability button on the site member's list.

3. The Availability button for each Friend on a user's Friendships tab on their profile.

4. The Chat toolbar that appears upper left for a logged-in user.

Thank you for your help & insight!