Chin implant: is it common not to use a screw fixture?

This is very common. You will find supporters of screw fixation of chin implants. IMO, this is unnecessary and every extra piece of hardware that we use during surgery can create potential issues/ complications down the road. Modern, anatomic type implants are long and fit into a very precise pocket along the jaw. As a result the risk of rotation and malposition of these implants is much lower than the older "cap" type implants. I hope this information is helpful for you.Stephen Weber MD, FACSDenver Facial Plastic Surgeon

The pocket is usually made under a thin but strong membrane called the periosteum with the pocket made to the exact size. The pocket then shrinks down around the implant to hold if firmly in place. A  a screw is not usually used for silicone implants (the most common type) but is used for others such as PTFE, Gortex, etc. 

In our practice, we use Silastic chin implants without screw fixation or application of any tapes. The chin implant procedure involves making a very precise pocket underneath the periosteum, and placing the implant directly between the bone and the periosteum itself. No screws or tape are  required. For more information, and many examples of chin implants, please see the link and video below