A self-contained system for drilling a drainhole laterally to a wellbore that includes a drill head with a tool for boring a drainhole and a self-propelled device for advancing the head into the drainhole during boring; a relay unit lowered into the wellbore, arranged to position the drill head against the sidewall of the wellbore in order to initiate the boring of the drainhole laterally to the wellbore; a cable for supplying electric power to the drill head, reeled out from the relay unit; and a mechanical system for removing cuttings from the drainhole during boring, the debris removed falling downhole.