This has now made it to the Ubuntu Kernels as of yesterday (11th June) so the Webcam support should be fixed with just an apt dist-upgrade in:xenial 4.4*artful 4.13*bionic 4.15* Maybe the Solution of this post should be updated to reflect this.
I got my dell xps yesterday. It is the developers edition that come with ubuntu 16.04 preinstalled.  I notice that cheese does not come installed, so I installed but no webcam is detected. I can see it if I do an lsusb, so I know is activated. I was wondering, does this laptop supports the webcam or not?   Edit: Good news, a dell engineer came and replace the monitor, that has the webcam integrated and presto, it is working now. Update: Most of the problems with the webcam is not hardware based. Looks like many of the laptops come with a firmware that the latest Linux kernel do not support at the moment. To solve the issue, Dell is replacing the whole monitor with a downgrade firmware of the webcam. If a less drastic solution is reported, I will update the post with it. Update2: Looks like there is a software solution now. 
Dell xps 13 9370 Webcam support