Cannot hear anyone on XBOXLIVE Party or Private chat or game lobby

What headset are you using? And give more information such as when it first happened and have you tried controller off/on reconnect etc?

sounds like its the headset or controller at fault to me, if you can try different head set then controller may need to send the headset back

another thing to try would be to change the voice to headset and tv (then you should hear the chat through the tv) to check the chat is working other than just the headset

Do you have a Chat pad plugged into your controller?

If so, unplug it and your problem should be solved.

If not, then i have no clue.

Just use Party Chat because more often than not anyone that talks in lobbies will be spouting off things you probably don't want to hear. And what if you do find more people that don't cuss are you just going to play private matches all the time?

When you're in a party make sure your character is switched to party chat and not game chat. You can check this by highlighting your character in the party app and then press A to select the game or party chat options.