If you are enrolled in Part A or B, the dose of pembrolizumab you receive will depend on when you join this study. The first group of participants will receive the lowest dose level of pembrolizumab. Each new group will receive a higher dose of pembrolizumab than the group before it, if no intolerable side effects were seen. This will continue until the highest tolerable dose of pembrolizumab is found. All participants will receive pembrolizumab during radiation therapy. The radiation will be to the chest area. In addition to pembrolizumab, participants in Part A will also receive either cisplatin and etoposide or carboplatin and etoposide.