The chemical abundances of exoplanet atmospheres may provide valuable information about the bulk compositions, formation pathways, and evolutionary histories of planets. Exoplanets which have large, relatively cloud-free atmospheres, and which orbit bright stars provide the best opportunities for accurate abundance measurements. For this reason, we measured the transmission spectrum of the bright (V~10.2), large (1.37RJ), sub-Saturn mass (0.19MJ) exoplanet WASP-127b across the near-UV to near-infrared wavelength range (0.3 - 5 microns), using the Hubble and Spitzer Space Telescopes. Our results show a feature-rich transmission spectrum, with absorption from Na, H2O, and CO2, as well as wavelength-dependent scattering from small-particle condensates, and a grey absorber which somewhat mutes the molecular absorption features. We ran two types of atmospheric retrieval models: one enforcing chemical equilibrium, and the other which fit the abundances freely. Our retrieved abundances at chemical equilibrium for Na, O and C are all super-solar, with abundances relative to solar values of 51+30-29, 23+15-9, and 33+43-25 respectively. Despite giving conflicting C/O ratios, both retrievals gave super-solar CO2 volume mixing ratios, which adds to the likelihood that WASP-127b's bulk metallicity is super-solar, since CO2 abundance is highly sensitive to atmospheric metallicity. In the future, spectroscopy with JWST will be able to constrain WASP-127b's C/O ratio, and may reveal the formation history of this metal-enriched, highly observable exoplanet.