Under Chat Log you can view the chats which have been sent either on your main event chat or individual session chats (by all guests). Select the drop down (as highlighted below) to choose the session you would like to view the Chat Log from:
Click the refresh icon to refresh the chat as needed (to see new messages come through) and you can delete any messages required by clicking on the trash can icon:
Update: There is now a 'Delete All' function where you can delete all existing chat log in the room with just one click.
Simply click the trash can icon the top right corner of the chat log to delete everything on the chat log section in one go.
Do note: only you (or team members with access to the event dashboard) can delete chat log messages from guests.