Uptake of diagnostic and therapeutic oligonucleotides that specifically target disease can be enhanced by attachment of a cell-penetrating peptide. Here, we describe the covalent attachment of an oligonucleotide to Tat, a biologically important cell-penetrating peptide, via click chemistry.Tat peptide has been shown to have excellent cell-penetrating properties. Here, we provide the first report on the modification of Tat peptide and oligonucleotides to form an oligonucleotide–peptide conjugate using copper-catalysed azide–alkyne cycloaddition. Highly denaturing conditions were used to ensure that the biomolecules were tethered covalently as opposed to electrostatically.