The distortion of light bundles from distant galaxies probes the statistical properties of the intervening inhomogeneous (dark) matter distribution. Its tidal gravitational field distorts the observable image shapes thereby causing a coherent ellipticity pattern (Cosmic Shear). The statistical properties of this pattern reflect those of the large-scale matter distribution in the Universe. Cosmic Shear can therefore probe the LSS without any reference to the relation between dark and luminous matter. Owing to the small magnitude of this effect, a reliable measurement of Cosmic Shear requires superb imaging of very faint objects. From our detailed and successful preliminary work on existing parallel imaging data with STIS, we have demonstrated that STIS provides the required image quality for this program due to its good pixel sampling and its small PSF anisotropy. We propose an imaging Parallel Program for Cycle 9, similar to that carried out in Cycle7. We propose to dedicate one and two orbit parallel opportunities to imaging with the 50CCD `Clear' filter. By combining the results from these two programs, we expect to measure the Cosmic Shear on the STIS angular scale with high precision. Comparison with light tracing through very large N-body simulations will allow us to constrain the cosmological parameters and fix the normalization of the dark matter power spectrum with high accuracy. We request parallel images with the STIS instrument, using the 50CCD `Clear filter'. In particular, we ask for observations during the parallel opportunities at the same pointing (within a few arcseconds) with total cummulative exposure time above 1600 seconds. This lower limit on exposure time has been derived empirically by analyzing available parallel STIS images: on 1600 second exposures, about 20 to 40 galaxy images per STIS field can be identified for which an ellipticity can be measured reliably (as determined, e.g., by comparing ellipticities measured with two different methods). In longer exposures, we will be able to measure the shapes of even more galaxy images. The shear analysis will be carried out for relatively high galactic latitude fields. In addition, we shall regularly need images of stellar fields, to monitor the stability of the PSF with time, e.g. through changes of the focus. Therefore, we do not restrict our observing request to only high galactic latitude fields. beginfigure*.ht begincenter <=avevmode vspace-0.0cm centerline\epsfigfile=plot1.tps, angle=-90, width= vspace-00.0 cm endcenter caption Histogram of the number of useful imaging frames (defined here that they have more than 300 seconds exposure time, CR-split, and proper guiding) per month. One sees that the number of frames useful for our program has decreased dramatically in the last year of the parallel program. endfigure* beginfigure*.ht begincenter <=avevmode vspace0.0cm centerline\epsfigfile=plot2.eps, angle=-90, width= vspace-00.0 cm endcenter caption Same as figure 2, except that we have plotted the exposure time used on all frames taken with the CLEAR `filter', together with those for which a cosmic ray split has been taken. endfigure* In the previous parallel program, a number of different exposure times for individual images have been used. From our pilot program, we have learned that the most suitable exposure times are 400 seconds per individual exposure, split into two read-outs for cosmic ray rejection. This CR-split is essential for obtaining accurate shape measurements of faint galaxy images. Exposure times substantially shorter than 400 seconds severely compromise the accurate relative alignment of individual exposures needed for the coaddition, whereas substantially longer exposure times hampers our ability to remove cosmic rays efficiently and can lead to a noticible effect of the differential velocity aberration which for the suggested exposures of 400 seconds is completely negligible. We will adopt a very similar exposure time for all of our observations. Why we propose an imaging STIS Parallel Program: Our proposal offers several crucial improvements over the way that STIS Pure Parallel Program images have been taken over the last year. Our aim is to both increase the number and the depth of available images using the CLEAR filter and to ensure that these images are not too affected by cosmic ray impacts and the blurring effects of relative velocity aberration. This is in contrast to the current implementation of the STIS Pure Parallel Program which since the end of October 1998 has been producing an ever decreasing number of data using the CLEAR filter. The CLEAR filter observed on average six times less than during the first year of the parallel program (see Fig.\ 2). The actual number of images taken in the CLEAR filter, using a CR-split mode, and with total integration time greater than 300 seconds has all but been reduced to zero since the end of 1998 (see Fig.\ 3). The use of a CR-split observing mode is crucial if one wants to optimally remove cosmic ray impacts and in order to limit the blurring effect of the relative velocity aberration affecting parallel instruments observations. Hence, the STIS Parallel Program as carried out since the beginning of 1999 no longer yields any useful data for the scientific program discussed here. Assuming N_ f fields all with the same number N_n\equiv N of galaxies, the relative accuracy with which the rms Cosmic Shear can be measured, using the estimator given in the caption to Fig.\ 1, is (see Schneider et al.\ 1998a) Delta=(square)rt<~ngle Gamma^2\rangle/ sqrtSigma(<~ngle Gamma^2\rangle) =2sqrtN_ f/ sqrtMu_4 +2(1+1/Rho)^2\;, where Rho=<~ngle Gamma^2\rangle N/Sigma_Epsilon^2, and Mu_4 is the kurtosis of Cosmic Shear on the angular scale under consideration. With an rms intrinsic ellipticity of Sigma_Epsilon~ 15\ these scales, Rho~ 1/2, showing that the sampling (or cosmic) variance is the largest contributor to the final uncertainty due to the non-Gaussian shear distribution. This is the reason for needing images along many independent lines-of-sight. The kurtosis will depend on the cosmological model, but is of order a few (Jain et al.\ 1999); more accurate estimates will be derived from further N-body simulations. Thus, the relative accuracy Delta will be between ~ sqrtN_ f/2 and ~ sqrtN_ f/3, depending on the number of usable galaxy images in the deeper images and on Mu_4. The reality of the signal will be checked with various tests. In order to reach our goal of an expected statistical uncertainty of the measurement of sqrt<~ngle Gamma^2\rangle of order 10\ we will need a total of ~ 500 useful pointings. Estimating that the current parallel program will provide us with ~ 100 useful (in terms of exposure time, background, lack of bright objects, etc) fields, the remaining fields can be obtained in about 1200 orbits; this latter number was estimated by assuming that 2/3 of the parallel orbits will be taken at relatively high galactic latitude, which are about equally split between one and two-orbit opportunities, and that about 80\ We would like to reiterate that this program cannot by carried out from the ground because the required number of independent (i.e., well separated) lines-of-sight which need to be imaged superbly both in quality and in depth can only be achieved with HST. Any accurate Cosmic Shear measurements from the ground will be restricted to larger angular scales, where the kurtosis, and thus the sampling variance, is smaller, the signal-to-noise Rho of a shear measurement per single field is larger, and where a sufficient number of stars are present on the field to map the (spatially dependent) PSF anisotropy. On such larger scales, the non- Gaussian effects which provide the best handle on Omega_0 will be very small and thus very difficult to measure accurately. Since the images obtained are expected to be useful for a wider range of scientific purposes, we require no proprietary period; as with the current parallel program, the data can be put into the archive immediately. In addition, we will make our processed images publicly available on the web. Images analyzed so far can be found at http://archive.eso.org/wdb/wdb/hst/shear\_result/form. With the expected statistical accuracy of the Cosmic Shear measurement from this parallel program, the redshift distribution of the galaxies becomes the major source of uncertainty in the quantitative interpretation of the data. Owing to the unusual spectral response of the 50CCD `filter', the measured magnitudes cannot easily be related to a standard photometric system. Therefore, additional color information for at least a subsample of the galaxies observed with STIS is needed. One of us (SS) is a member of a GTO team which is carrying out deep photometric imaging with VLT/FORS in 6 optical filters with a total integration time of 3 nights, which will be supplemented by IR imaging on VLT/ISAAC. In addition, we expect to directly image several STIS fields with the ESO VLT in several optical and IR wavebands, using the FORS and ISAAC instruments. These multi- color data, with an exposure time of ~ 2 hours per filter, will be sufficiently deep to yield fairly accurate redshift estimates for most of the galaxies for which an ellipticity measurement is used in the Cosmic Shear analysis.