I've asked this back when support was responding to user queries. There does not appear to be a way.
I now have so many messages the chat tab will not load and is permanently blank.
There is a work around for the slow loading chat. Don't enter through the chat page. Start a relay and start your conversation through the race page, or the waiting for their turn list. It may also work with the leader board.
The draw back is you may miss what the conversation is in the window until after you have sent the first message.