Your Xbox Live settings control what you can and can't see in chat. It's possible that you've (accidentally) turned off seeing chat messages. Resolving this is simple:

Make sure you log in to the Xbox Accounts website with the account you use to play Minecraft. You may need to quit and restart the Minecraft app for it to pick up your new Privacy settings.

If your account is controlled by a parent or guardian, they will have to make the above change for you. If they intentionally turned off this setting, there is NO way around it.