At this time, private messages on Chat aren't available.
If you're a writer and have Chat enabled on your publication, you can start a thread for just your paid subscribers or a thread with all your subscribers.
Threads that are for paid subscribers will appear blurred for free subscribers.
If free subscribers try to access a paid thread, the app will let them know that it's only for paid subscribers. They'll be shown a link where they can manage their subscriptions on their Substack account and upgrade to a paid subscription.
You can also try reader participation on Chat where you can select which type of reader can initiate and start a conversation on your publication's Chat.