A dual string drilling system for drilling a well bore in an earth formation, having a rotatable, tubular outer drill string and an upper rotatable, tubular inner drill string. An elongate tubular drill bit is mounted to a distal end of the outer drill string. The tubular drill bit having an interior passageway having a longitudinal axis which is inclined with respect to the longitudinal axis of the outer drill string. The drill bit is further provided with a cutaway portion extending through a wall of the tubular outer drill string. A lower rotatable inner drill string is coupled to the upper rotatable tubular inner drill string and is disposed within the interior passageway of the drill bit. A second drill bit is mounted to the distal of the lower inner drill string and is sized to extend beyond the drill bit mounted to the outer drill string.