We present an optical to near-infrared transmission spectrum of the hot Jupiter HAT-P-1b, based on HST observations, covering the spectral regime from 0.29 to 1.027{mu}m with STIS, which is coupled with a recent WFC3 transit (1.087 to 1.687{mu}m). We derive refined physical parameters of the HAT-P-1 system, including an improved orbital ephemeris. The transmission spectrum shows a strong absorption signature shortward of 0.55{mu}m, with a strong blueward slope into the near-ultraviolet. We detect atmospheric sodium absorption at a 3.3{sigma} significance level, but find no evidence for the potassium feature. The red data implies a marginally flat spectrum with a tentative absorption enhancement at wavelength longer than ~0.85{mu}m. The STIS and WFC3 spectra differ significantly in absolute radius level (4.3 +/- 1.6 pressure scale heights), implying strong optical absorption in the atmosphere of HAT-P-1b. The optical to near-infrared difference cannot be explained by stellar activity, as simulta- neous stellar activity monitoring of the G0V HAT-P-1b host star and its identical companion show no significant activity that could explain the result. We compare the complete STIS and WFC3 transmission spectrum with theoretical atmospheric mod- els which include haze, sodium and an extra optical absorber. We find that both an optical absorber and a super-solar sodium to water abundance ratio might be a sce- nario explaining the HAT-P-1b observations. Our results suggest that strong optical absorbers may be a dominant atmospheric feature in some hot Jupiter exoplanets.
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