We present Hubble Space Telescope near-infrared transmission spectroscopy of the transiting hot-Jupiter HAT-P-1b. We observed one transit with Wide Field Camera 3 using the G141 low-resolution grism to cover the wavelength range 1.087- 1.678 {mu}m. These time series observations were taken with the newly available spatial scan mode that increases the duty cycle by nearly a factor of two, thus improving the resulting photometric precision of the data. We measure a planet-to-star radius ratio of Rp/R*=0.11709+/-0.00038 in the white light curve with the centre of transit occurring at 2456114.345+/-0.000133 (JD). We achieve S/N levels per exposure of 1840 (0.061%) at a resolution of {Deltalambda}=19.2nm (R~70) in the 1.1173 - 1.6549{mu}m spectral region, providing the precision necessary to probe the transmission spectrum of the planet at close to the resolution limit of the instrument. We compute the transmission spectrum using both single target and differential photometry with similar results. The resultant transmission spectrum shows a significant absorption above the 5-{sigma} level matching the 1.4{mu}m water absorption band. In solar composition models, the water absorption is sensitive to the ~1 mbar pressure levels at the terminator. The detected absorption agrees with that predicted by an 1000 K isothermal model, as well as with that predicted by a planetary-averaged temperature model.
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