We employ Real-Time Time-Dependent Density Functional Theory to study hole oscillations within a B-DNA monomer (one base pair) or dimer (two base pairs). Placing the hole initially at any of the bases which make up a base pair, results in THz oscillations, albeit of negligible amplitude. Placing the hole initially at any of the base pairs which make up a dimer is more interesting: For dimers made of identical monomers, we predict oscillations with frequencies in the range $f approx$ 20-80 THz, with a maximum transfer percentage close to 1. For dimers made of different monomers, $f approx$ 80-400 THz, but with very small or small maximum transfer percentage. We compare our results with those obtained recently via our Tight-Binding approaches and find that they are in good agreement.