A drilling fluid comprising a blend of brine and additives for maintaining rheological properties in a neutral or slightly acidic brine and a method for using the drilling fluid to drill into a producing formation are disclosed. The drilling fluid comprises viscosifying polymer and fluid loss polymer that function in the brine without substantially adversely affecting their properties. The brine is substantially free of insoluble solids. The viscosifying polymer and/or the fluid loss control polymer can be acid soluble. Zinc salts in the form of zinc bromide alone or in a mixture of zinc bromide and calcium bromide are added to increase the density of the brine solution. The viscosifying polymer has pendant amide and sulfonic acid or sulfonate groups. Alternatively or additionally, the viscosifying polymer comprises a polysaccharide. The fluid loss control polymer can comprise a cross-linked, cationic or amphoteric starch. Soluble solids are dispersed in the brine.