Which cameras and browsers work
Anything a browser can see. A built-in laptop webcam, a USB camera, a phone's front or back camera, and virtual cameras such as OBS all work, because ChessChat asks the browser for a video device rather than talking to hardware itself. If your camera works in a video call, it works here.
On the software side that means Chrome, Edge, Firefox and Safari, on Windows, macOS, Linux, iOS and Android. Phones are not an afterthought: the layout is built for a portrait screen, the front camera is the default, and the site can be installed to your home screen so it opens without browser furniture around it.
What the camera is used for, and what it is not
It is sent live to the person you are playing, and to nobody else. Streams are not recorded and not stored, there is no archive of past games' video, and the server does not sit in the middle of the picture: the media goes peer to peer over WebRTC where it can.
The single exception is written into the privacy policy rather than buried here. When one player reports another, one still frame of the reported player's camera is captured so a human being can act on the report. That is the only circumstance in which any frame of your video is kept.
If you would rather not be seen
ChessChat is played face to face, so a clear camera is how you get a game, and there is no setting that hides you while you play. If that is not for you, there are plenty of good chess sites where nobody sees anybody.
If the worry is the room rather than the face, an unmade bed or a kitchen, sit with a plain wall behind you. And if somebody walks in, switch the camera off for a moment and turn it back on when you are ready.
When the camera will not start
Almost always something else has it. Video calls hold a camera exclusively on most systems, so a Zoom or Teams window in the background is the usual culprit, followed by a second tab of ChessChat itself. Close the other user of the camera and reload.
After that, check the browser has permission: every browser keeps a per-site camera setting, and a refusal earlier can be quietly remembered forever. ChessChat tells you which of these it is rather than showing a dark rectangle, because a blank tile that could mean four different things is not an error message.