Patients with cancer have a high risk of developing venous blood clots or thromboembolism (VTE). In an effort to target patients at highest risk of VTE for thromboprophylaxis (protective treatment for blood clots), numerous studies have identified serum biomarkers for risk of future VTE. There is also increasing evidence pointing to a prophylactic effect of statin therapy on the risk of developing VTE in high-risk populations including patients with advanced cancer. The purpose of this research study is to find out whether treatment with rosuvastatin (the study drug) reduces the risk of VTE in patients with cancer receiving chemotherapy. This study is specifically investigating the impact of rosuvastatin therapy on serum biomarkers (D-dimer and others) that indicate a risk for VTE, as well as safety and tolerance of rosuvastatin therapy in this population.