A cooling system for the fillet of a turbine blade is provided. The blade includes an airfoil transitioning to a platform having a flow path surface. The transition region is defined by a fillet. A cooling passage is formed in the platform and extends about at least a portion of the periphery of the airfoil. The cooling passage is located proximate to the flow path surface and is substantially aligned with at least a portion of the fillet. Coolant is delivered to the passage by a supply hole, which can reduce the temperature in the fillet region. As a result, thermal gradients in the fillet region can be minimized, which can reduce thermal stresses. An exhaust hole extends between the passage and the flow path surface of the platform. Thus, coolant discharged from the exhaust holes enters the flow path of the turbine.