The molecule-based chiral spin chain, [Cu(pyrimidine)(H2O)4]SiF6·H2O exhibits staggered g-tensors, a rich low-temperature excitation spectrum and a spin gap that opens on application of magnetic field. These phenomena are reminiscent of those previously observed in non-chiral staggered chains, which are explicable within the sine-Gordon (SG) quantum-field theory. In our case, however, the size of the gap and its measured linear field dependence do not fit with the SG model as it stands. We have proposed that the differences arise due to additional terms in the Hamiltonian resulting from the chiral structure, particularly a uniform Dzyaloshinskii-Moriya coupling and a four-fold periodic staggered field. These proposals can be confirmed via determination of the static magnetic structure of the gapped ground state that exists at low temperatures under small applied magnetic fields.