Can psychiatrists also treat chronic pain?

Yes: Pain affects all aspects of one's life. In chronic situations, pain may have devastating effect on a patient's emotional well-being. A psychiatrist or a psychologist can help patient deal much more effectively with depression, anxiety, etc. They can also help with improving patient's coping skills.

Yes: Some psychiatrists do treat pain. They can use cognitive and behavioural therapy as well as medications. They can't use injections however.