Weak lensing by large-scale structure provides a unique method to directly measure matter fluctuations in the universe , and has recently been detected from the ground . Here , we report the first detection of this ‘ cosmic shear ’ based on space-based images . The detection was derived from the Hubble Space Telescope ( HST ) Survey Strip ( or “ Groth Strip ” ) , a 4 ^ { \prime } \times 42 ^ { \prime } set of 28 contiguous WFPC2 pointings with I < 27 . The small size of the HST Point-Spread Function ( PSF ) affords both a lower statistical noise , and a much weaker sensitivity to systematic effects , a crucial limiting factor of cosmic shear measurements . Our method and treatment of systematic effects were discussed in an earlier paper ( Rhodes , Refregier & Groth 2000 ) . We measure an rms shear of 1.8 % on the WFPC2 chip scale ( 1.27 ’ ) , in agreement with the predictions of cluster-normalized CDM models . Using a Maximum Likelihood ( ML ) analysis , we show that our detection is significant at the 99.5 % confidence level ( CL ) , and measure the normalization of the matter power spectrum to be \sigma _ { 8 } \Omega _ { m } ^ { 0.48 } = 0.51 ^ { +0.14 } _ { -0.17 } , in a \Lambda CDM universe . These 68 % CL errors include ( Gaussian ) cosmic variance , systematic effects and the uncertainty in the redshift distribution of the background galaxies . Our result is consistent with earlier lensing measurements from the ground , and with the normalization derived from cluster abundance . We discuss how our measurement can be improved with the analysis of a large number of independent WFPC2 fields .