In combination a drilling mast and a top drive system for a drilling rig having a drill floor with a well center. The drilling mast has a U-shaped horizontal cross section with a left-hand mast wall, a rear mast wall, and a right-hand mast wall, and with an open front side. Each of the mast walls is provided with one or more vertical rails that are, in use of the drilling rig, parallel to a vertical firing line that extends through the well center. The top drive system comprises a traveling carriage and a top drive unit supported by said carriage. A left-hand fingerboard device is mounted to the left-hand mast wall and a right-hand side fingerboard device is mounted to the right-hand mast wall.