Abstract: A reamer apparatus is adapted for use in combination with a radial whipstock assembly in drilling a curved bore in a subsurface formation at a predetermined angle of build. The reamer apparatus is comprised of a drill bit, at least one articulated joint or drill collar connected to the lower end of the drill string, and a stabilized reamer interconnected for rotation behind the drill bit which includes cutter blades overgauged in relation to the drill bit and projecting substantially in outward radial directions from the reamer body, each blade having an elongated cutting edge which extends substantially parallel to the direction of drilling and a stabilized leading end so as to stabilize the reamer and avoid preferential cutting as the drill bit proceeds along the desired course.