A method and associated apparatus for lateral drilling in an oil and/or gas well involving either stopping the drilling or temporarily cementing in a plug in the existing well bore at the desired location for deviation. A tight radius of curvature is then rotary drilled by use of a flexible drilling collar made up of a series of short drill string sections interconnected by universal joints that terminate within an eccentric collar on the final drill string section. The eccentric collar is equipped with a sidewall engaging means to hold the eccentric collar from rotating during rotary drilling. A flexible collar (e.g., ball and socket) extending outwardly and downwardly from the far end of the final drill string section passing through the eccentric collar connects to a drill bit collar and rotary drill bit. A stabilizer/reamer of essentially the same size or slightly larger diameter than the drill bit surrounds the drill bit collar, thus producing a fulcrum for tilting the drill bit perpendicular to the well bore. The eccentric collar on the last drill string section that engages the well bore forces the deflection of the drill bit about the fulcrum and holds this orientation as the rotating drill proceeds forward. Such a technique can achieve a twelve foot radius of curvature in an existing oil or gas well bore for establishing lateral drain holes essentially horizontal to the otherwise vertical well bore.