An apparatus and method for damping vibration, especially torsional vibration due to stick-slip, in a drill string, Sensors measure the instantaneous angular velocity of the drill string at one or more locations along the length of the drill string. One or more vibration damping modules are also spaced along the length of the drill string. When torsional vibration above a threshold is detected, the damping module imposes a reverse torque on the drill that dampens the torsional vibration. The reverse torque can be created by imparting a frictional resistance to the rotation of the drill string. The frictional resistance can be created externally, by extending friction pads from the damping module so that they contact the bore hole wall and drag along the bore hole as the drill string rotates, or internally by anchoring a housing mounted on the drill string to the wall of the bore hole and then imposing frictional resistance on a fluid, such as a magnetorheological fluid, flowing within the drill string.