Additional Study Information: This study is for adults who have non-small cell lung cancer and have had surgery to remove their lung tumor. People who have lung cancer and undergo surgery still have a significant risk of their cancer returning outside of the lung. The purpose of this study is to determine if a new type of immune-based therapy can increase your chance of being cured. Chemotherapy is usually given after surgery to reduce the risk of the cancer returning. Despite aggressive surgery and chemotherapy, the risk of lung cancer recurrence remains high in most patients. This study aims to determine if a novel immune therapy consisting of two drugs is feasible and potentially increases the chance of cure in lung cancer patients after surgery and standard chemotherapy. The immune-based therapy being given in this study consists of two medications nameddurvalumab and tremelimumab. These medications are both given intravenously once every four weeks. The medications being given in this study has previously been tested in patients with more advanced cancer. These studies have demonstrated that the immune-based therapy with durvalumab and tremelimumab can be given safely to patients with manageable side-effects.