The chemical abundances of exoplanet atmospheres may provide valuable information about the bulk compositions, formation pathways, and evolutionary histories of planets. Exoplanets with 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 (1.37 R$_{J}$), sub-Saturn mass (0.19 M$_{J}$) exoplanet WASP-127b across the near-UV to near-infrared wavelength range (0.3 - 5 $mu$m), using the Hubble and Spitzer Space Telescopes. Our results show a feature-rich transmission spectrum, with absorption from Na, H$_{2}$O, and CO$_{2}$, and wavelength-dependent scattering from small-particle condensates. 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 9$^{+15}_{-6}$, 16$^{+7}_{-5}$, and 26$^{+12}_{-9}$ respectively. Despite giving conflicting C/O ratios, both retrievals gave super-solar CO$_{2}$ volume mixing ratios, which adds to the likelihood that WASP-127bs bulk metallicity is super-solar, since CO$_{2}$ abundance is highly sensitive to atmospheric metallicity. We detect water at a significance of 13.7 $sigma$. Our detection of Na is in agreement with previous ground-based detections, though we find a much lower abundance, and we also do not find evidence for Li or K despite increased sensitivity. In the future, spectroscopy with JWST will be able to constrain WASP-127bs C/O ratio, and may reveal the formation history of this metal-enriched, highly observable exoplanet.