A water-base drilling fluid for use in drilling wells through a formation containing a shale which swells in the presence of water. The drilling fluid preferably includes: an aqueous based continuous phase, a weight material, and a shale hydration inhibition agent having the formula: H2N—R—{OR′}x—Y in which R and R′ are alkylene groups having 1 to 6 carbon atoms and x is a value from about 1 to about 25. The Y group should be an amine or alkoxy group, preferably a primary amine or a methoxy group. The shale hydration inhibition agent should be present in sufficient concentration to reduce the swelling of the shale. Also inclusive of the present invention is a method of reducing the swelling of shale clay encountered during the drilling of a subterranean well, the method comprising circulating in the well a water-base drilling fluid formulated in accordance with the present invention.