This is a Phase I study to assess the safety and MTD of paclitaxel + ribociclib (LEE011) in patients with Rb+, advanced breast cancer. Dose escalation will be performed using standard 3 + 3 dosing strategy. The starting dose of ribociclib (LEE011) is 200 mg once daily; dose escalation proceeds in 200 mg increments up to a maximum of 600 mg. Dose-limiting toxicities (DLT) will be based upon first-cycle toxicity.