Weak lensing by large-scale structure allows a direct measure of the dark matter distribution. We have used parallel images taken with the Space Telescope Imaging Spectrograph (STIS) on the Hubble Space Telescope to measure weak lensing, or cosmic shear. We measure the shapes of 26036 galaxies in 1292 STIS fields and measure the shear variance at a scale of 0.51 arcminutes. The charge transfer efficiency (CTE) of STIS has degraded over time and introduces a spurious ellipticity into galaxy shapes during the readout process. We correct for this effect as a function of signal to noise and CCD position. We further show that the detected cosmic shear signal is nearly constant in time over the approximately four years of observation. We detect cosmic shear at the 5.1 sigma level, and our measurement of the shear variance is consistent with theoretical predictions in a LambdaCDM universe. This provides a measure of the normalization of the mass power spectrum sigma_8=(1.02 +- 0.16) (0.3/Omega_m)^{0.46} (0.21/Gamma)^{0.18}$. The one-sigma error includes noise, cosmic variance, systematics and the redshift uncertainty of the source galaxies. This is consistent with previous cosmic shear measurements, but tends to favor those with a high value of sigma_8. It is also consistent with the recent determination of sigma_8 from the Wilkinson Microwave Anisotropy Probe (WMAP) experiment.
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