New analogs of the commercial asymmetric monomethine cyanine dyes thiazole orange (TO) and thiazole orange homodimer (TOTO) with hydroxypropyl functionality were synthesized and their properties in the presence of different nucleic acids were studied. The novel compounds showed strong, micromolar and submicromolar affinities to all examined DNA ds-polynucleotides and poly rA–poly rU. The compounds studied showed selectivity towards GC-DNA base pairs over AT-DNA, which included both binding affinity and a strong fluorescence response. CD titrations showed aggregation along the polynucleotide with well-defined supramolecular chirality. The single dipyridinium-bridged dimer showed intercalation at low dye-DNA/RNA ratios. All new cyanine dyes showed potent micromolar antiproliferative activity against cancer cell lines, making them promising theranostic agents.