As a moderator, you can restrict participants to chat privately.

Go to Settings in the navigation bar.

A popup window will appear showing three categories, go to  PARTICIPANTS > Can chat privately.

Turn it on to allow participants to chat privately during the session.

Turn it off to prevent participants from chatting privately during the session.

This will only affect participants.
Other moderators in the session can still chat privately between them during the session.
These settings have no effect in Rooms since all users become moderators there.