Sequence-specific phosphorothioate oligonucleotides comprising nucleoside units which are joined together by either substantially all Sp or substantially all Rp phosphorothioate intersugar linkages are provided. Such sequence-specific phosphorothioate oligonucleotides having substantially chirally pure intersugar linkages are prepared by enzymatic or chemical synthesis. Sequence-specific phosphorodithioate oligonucleotides are also provided. Such sequence-specific phosphorodithioate oligonucleotides are prepared by chemical synthesis. They are especially well suited as diagnostics, therapeutics and research reagents.