The geometrical, chemical and ferroelectric properties of a new nanoscale short-period three-component SrTiO3/BaTiO3/PbTiO3 perovskite superlattice are investigated using a first principles density functional approach. The study focuses on varying the thickness of each component in the superlattice and determining the resulting lattice distortion and total polarization. Thicknesses of up to three unit cells in a single component are considered and the in-plane lattice constants normal to the [001] stacking direction are fixed to the bulk SrTiO3 values to simulate a rigid substrate. It is found that the PbTiO3 layers play a key role in strain and polarization enhancement. By increasing the amount of PbTiO3 in the superlattices the strain in the other components increases significantly resulting in an enhanced total polarization of the superlattice relative to bulk BaTiO3. Increasing the number of BaTiO3 layers also improves the overall polarization. All the SrTiO3 layers in each superlattice are found to be highly polarized. Many of the calculated features are similar to those found previously by others for the SrTiO3/BaTiO3/CaTiO3 superlattice, although in the present study significantly greater enhancement factors and polarization values are found. The predicted enhancement of the polarization is mostly attributed to lattice strain due to mismatch of the in-plane lattice constant of the three-component materials.