The stabilizer disclosed includes a body for mounting on the drill string and a sleeve for mounting on the body to engage the wall of the well bore. The body is mounted eccentrically of the longitudinal axis of the drill string and the sleeve is mounted eccentrically to the longitudinal axis of the body. The eccentricities of the body and the sleeve are equal so that when positioned where the eccentricities extend in the opposite direction, the sleeve will be centrally located with respect to the drill string and will tend to hold the drill string in the center of the well bore, whereas when the body and sleeve are rotated relatively so that the eccentricities of the two members accumulate, the sleeve will then be positioned with its longitudinal axis spaced from the longitudinal axis of the drill string and the sleeve will exert a lateral force on the drill string urging the drill string away from the center of the well bore.