High affinity, chemically modified triplex-forming oligonucleotides (TFOs) and methods for use thereof are disclosed. TFOs are defined as triplex-forming oligonucleotides which bind as third strands to duplex DNA in a sequence specific manner. Triplex-forming oligonucleotides may be comprised of any possible combination of nucleotides and modified nucleotides. Modified nucleotides may contain chemical modifications of the heterocyclic base, sugar moiety or phosphate moiety. A high affinity oligonucleotide (K.sub.d.ltoreq.2.times.10.sup.-8) which forms a triple strand with a specific DNA segment of a target gene DNA is generated. It is preferable that the K.sub.d for the high affinity oligonucleotide is below 2.times.10.sup.-10. The nucleotide binds or hybridizes to a target sequence within a target gene or target region of a chromosome, forming a triplex region. The binding of the oligonucleotide to the target region stimulates mutations within or adjacent to the target region using cellular DNA synthesis, recombination, and repair mechanisms. The mutation generated activates, inactivates, or alters the activity and function of the target gene.