Nanowires (NWs) hold great potential in advanced thermoelectrics due to their reduced dimensions and low-dimensional electronic character. However, unfavorable links between electrical and thermal conductivity in state-of-the-art unpassivated NWs have, so far, prevented the full exploitation of their distinct advantages. A promising model system for a surface-passivated one-dimensional (1D)-quantum confined NW thermoelectric is developed that enables simultaneously the observation of enhanced thermopower via quantum oscillations in the thermoelectric transport and a strong reduction in thermal conductivity induced by the core-shell heterostructure. High-mobility modulation-doped GaAs/AlGaAs core-shell NWs with thin (sub-40 nm) GaAs NW core channel are employed, where the electrical and thermoelectric transport is characterized on the same exact 1D-channel. 1D-sub-band transport at low temperature is verified by a discrete stepwise increase in the conductance, which coincided with strong oscillations in the corresponding Seebeck voltage that decay with increasing sub-band number. Peak Seebeck coefficients as high as ≈65-85 µV K-1 are observed for the lowest sub-bands, resulting in equivalent thermopower of S2 σ ≈ 60 µW m-1 K-2 and S2 G ≈ 0.06 pW K-2 within a single sub-band. Remarkably, these core-shell NW heterostructures also exhibit thermal conductivities as low as ≈3 W m-1 K-1 , about one order of magnitude lower than state-of-the-art unpassivated GaAs NWs.