We report measurements of the CMB polarization power spectra from the January 2003 Antarctic flight of BOOMERANG. The primary results come from six days of observation of a patch covering 0.22% of the sky centered near R.A. = 82.5 deg., Dec= -45 deg. The observations were made using four pairs of polarization sensitive bolometers operating in bands centered at 145 GHz. Using two independent analysis pipelines, we measure a non-zero <EE> signal in the range 100< l <1000 with a significance 4.8-sigma, a 2-sigma upper limit of 8.6 uK^2 for any <BB> contribution, and a 2-sigma upper limit of 7.0 uK^2 for the <EB> spectrum. Estimates of foreground intensity fluctuations and the non-detection of <BB> and <EB> signals rule out any significant contribution from galactic foregrounds. The results are consistent with a Lambda-CDM cosmology seeded by adiabatic perturbations. We note that this is the first detection of CMB polarization with bolometric detectors.