Recent experimental studies of magnetic domain expansion under easy-axis drive fields in materials with a perpendicular magnetic anisotropy have shown that the domain wall velocity is asymmetric as a function of an external in-plane magnetic field. This is understood as a consequence of the inversion asymmetry of the system, yielding a finite chiral Dzyaloshinskii-Moriya interaction. Numerous attempts have been made to explain these observations using creep theory, but, in doing so, these have not included all contributions to the domain wall energy or have introduced additional free parameters. In this article we present a theory for creep motion of chiral domain walls in the creep regime that includes the most important contributions to the domain-wall energy and does not introduce new free parameters beyond the usual parameters that are included in the micromagnetic energy. Furthermore, we present experimental measurements of domain wall velocities as a function of in-plane field that are well described by our model, and from which material properties such as the strength of the Dzyaloshinskii-Moriya interaction and the demagnetization field are extracted.