According to the invention, a downhole anchor assembly is employed for absorbing reaction torque from a downhole mud motor in a directional drill string so as to minimize azimuthal deviation from such reaction torque.

The anchor assembly has as its main structural basis an elongated, generally cylindrical housing with upper and lower ends formed as tool joints for coupling the body into a directional drill string. Three elongated chain support bodies are longitudinally mounted in the housing, evenly circumferentially spaced about the periphery, and each support body supports an endless anchor block chain so that elongated portions of the chains are longitudinally arranged and generally radially exposed externally of the bodies.

The chain support bodies are radially shiftable under the influence of hydraulic drilling fluid pressure from retracted positions in the body to extended positions in which the exposed chain portions grip the well casing against twisting of the drill string.