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For solar-system objects, ultraviolet spectroscopy has been critical in identifying sources for stratospheric heating and measuring the abundances of a variety of hydrocarbon and sulfur-bearing species, produced via photochemical mechanisms, as well as oxygen and ozone. To date, less than 20 exoplanets have been probed in this critical wavelength range (0.2-0.4 um). Here we use data from Hubble's newly implemented WFC3 UVIS G280 grism to probe the atmosphere of the hot Jupiter HAT-P-41b in the ultraviolet through optical in combination with observations at infrared wavelengths. We analyze and interpret HAT-P-41b's 0.2-5.0 um transmission spectrum using a broad range of methodologies including multiple treatments of data systematics as well as comparisons with atmospheric forward, cloud microphysical, and multiple atmospheric retrieval models. Although some analysis and interpretation methods favor the presence of clouds or potentially a combination of Na, VO, AlO, and CrH to explain the ultraviolet through optical portions of HAT-P-41b's transmission spectrum, we find that the presence of a significant H- opacity provides the most robust explanation. We obtain a constraint for the abundance of H-, log(H-) = -8.65 +/- 0.62 in HAT-P-41b's atmosphere, which is several orders of magnitude larger than predictions from equilibrium chemistry for a 1700 - 1950 K hot Jupiter. We show that a combination of photochemical and collisional processes on hot hydrogen-dominated exoplanets can readily supply the necessary amount of H- and suggest that such processes are at work in HAT-P-41b and many other hot Jupiter atmospheres.