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, Tap the 'Speech Bubble' in the top right corner to open the messenger pane.
Then tap on the "Contest" option.
This will bring up a list of your active contest. Tapping on one of the contests listed here will open up the group chat with only the people entered in that contest.