The app is not showing direct option for chat. I have to open browser to get to chat. When I tap chat option, window comes to open it with app or with browser; when I tap for app, it opens browser.
This is currently a status-deferred feature request on Meta Stack Exchange, and there's a corresponding iOS version of the question there (which is generally the place where major requests for changes to the software are best pitched, though they can also be posted here), and it doesn't look like it is particularly high on the list of priorities on the development schedule. If you really want this, those feature requests are the places to add pressure (votes, answers saying why it is critical, bounties, etc.).