Does something like this exist?

I just got a TV and I want to hook my Xbox up to it. The thing is, is that it's already hooked up to a 144hz monitor so I can have 120fps on Xbox. Is there a device out there that I can hook up my Xbox to my TV and monitor and keep 120fps on my monitor and still be able to use it for my TV? (If there is a better place to ask this, please tell me)