The present invention relates to latices of sulfonated thermoplastic polymers which function as viscosification agents when added to oil-based drilling muds which are the fluids used to maintain pressure, cool drill bits and lift cuttings from the holes in the drilling operation for oil and gas wells. The sulfonated thermoplastic polymer of the latex has about 5 to about 100 meq. of sulfonate groups per 100 grams of the sulfonated thermoplastic polymer, wherein the sulfonated groups are neutralized with a metallic cation or an amine or ammonium counterion. A polar cosolvent can optionally be added to the mixture of oil drilling mud and sulfonated polymer, wherein the polar cosolvent increases the solubility of the sulfonated polymer in the oil drilling mud by decreasing the strong ionic interactions between the sulfonate groups of the sulfonated polymer.