We present new results on the shock around the south-west radio lobe of Centaurus A using data from the Chandra Very Large Programme observations (740 ks total observing time). The X-ray spectrum of the emission around the outer south-western edge of the lobe is well described by a single power-law model with Galactic absorption – thermal models are strongly disfavoured, except in the region closest to the nucleus. We conclude that a significant fraction of the X-ray emission around the south-west part of the lobe is synchrotron, not thermal. We infer that in the region where the shock is strongest and the ambient gas density lowest, the inflation of the lobe is accelerating particles to X-ray synchrotron emitting energies, similar to supernova remnants such as SN1006. This interpretation resolves a problem of our earlier, purely thermal, interpretation for this emission, namely that the density compression across the shock was required to be much larger than the theoretically expected factor of 4. We describe a self-consistent model for the lobe dynamics and shock properties using the shell of thermal emission to the north of the lobe to estimate the lobe pressure. Based on this model, we estimate that the lobe is expanding to the south-west with a velocity of ∼2600 km s−1 , roughly Mach 8 relative to the ambient medium. We discuss the spatial variation of spectral index across the shock region, concluding that our observations constrain γmax for the accelerated particles to be ∼108 at the strongest part of the shock, consistent with expectations from diffusive shock acceleration theory. Finally, we consider the implications of these results for the production of ultra-high energy cosmic rays (UHECRs) and TeV emission from Centaurus A, concluding that the shock front region is unlikely to be a significant source of UHECRs, but that TeV emission from this region is expected at levels comparable to current limits at TeV energies, for plausible assumed magnetic field strengths.