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.[H+B−]d in which R and R′ are alkylene groups having 1 to 6 carbon atom 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 acid H+B− is a protic acid selected from the group consisting of inorganic acids and organic acids, illustrative examples of which include: hydrochloric, hydrobromic, sulfuric, phosphoric, nitric, boric, perchloric, formic, acetic, halogenated acetic, propionic, butyric, maleic, fumeric, glycolic, lactic, citric and combinations of these. 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.