First off, do you know what it cut itself on? I would do a complete check of your chick housing and remove all dangerous objects,(protruding nails, screws, boards,etc...) so this won't happen with any more of your chicks. Second, preventing infection here is key. the wound needs to be cleaned and disinfected but not covered. Wet breeds bacteria and invites all kinds of nastiness you don't want. Iodine Tincture is an excellent disinfectant and has the added benefit of disguising the freshness of the wound. I don't think you need to stitch the wound because it is already fairly jagged and the bleeding is stopped. It should close up fairly well but I would continue to disinfect it and watch for infection regularly. As an added precaution adding some antibiotics to the chicks water may not be a bad idea to head off any infection before it takes hold. ** Watch the other chicks carefully around him for a while. If they are pecking the wound you may need to separate him.
If you discover what it cut itself on, it could change things a tiny bit. Good luck!!