Webcam software with live chroma keying/green screen

After some help I found that the easiest way to accomplish this is by using Open Broadcaster Software:

Free and open source software for video recording and live streaming. Download and start streaming quickly and easily on Windows, Mac or Linux.

After installing and launching the software click on the + button under Sources to add your webcam as an input source.

Give your input a name in case you'll be using multiple camera inputs. Choose your webcam (if you have more than one) and then press OK. Back in the main window right click on the webcam source and select Filters

Press on the + button under Effect Filters and select Chroma Key and give it a new name.

From here you can select the colour that you wish to remove. You can choose from the presets or choose your own colour.

To see the full effect you'll need to have something in the background. In the main window select a new source. You can choose an image, video or additional camera.

Now you'll see the media source appear behind your webcam!