The LS30 and LS40 are wireless universal gaming headsets. As such, they work on both the Playstation and Xbox consoles. When using these headsets with the Xbox One, you need to connect the chat cable to the controller in order to use chat. If you're not using chat, you can leave the cable disconnected.
The chat cable on Xbox is a requirement when a headset is universal and works on both platforms. The only headsets that can use chat without the chat cable are Xbox One only licensed headsets.