Upon entering the Matchup page, you will notice a set of options near the top right of the page. Click on the one labeled "Contest Chat" to bring up that specific contest's chat panel.
You can also access the chat by opening The Messenger in the bottom right corner. From here you can select the contest option and choose which group chat you wish to open.
On any screen in the App, Tap the 'Speech Bubble' in the top right corner to open your Messenger.
Then tap on the 'Contest' option.
This will bring up a list of your active contest. From here you can choose which group chat you would like to open by tapping on said group.