For drilling a hole and machining at least its opening end without changing tools, a through-hole is drilled using a special tool, and then the same tool is moved sideways by means of a special chuck which guides the tool during machining of the drilled hole. The chuck has a locking means which when engaged holds it in a drilling position and which when disengaged allows sideways motion of a tool mounted in the chuck. The longitudinal section of the tool used, to be located within the hole during the machining operation, is situated within a curved surface having a radius just as great as that of the drill and having its center of curvature on the line about which the tool rotates during drilling.