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We report measurements of the CMB polarization power spectra from the 2003 January Antarctic flight of BOOMERANG. The primary results come from 6 days of observation of a patch covering 0.22% of the sky centered near RA= 82 fdg 5, decl.=-45. 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 nonzero⟨ EE⟩ signal in the range 201< l< 1000 with a significance of 4.8 σ, a 2 σ upper limit of 8.6 μK 2 for any⟨ BB⟩ contribution, and a 2 σ upper limit of 7.0 μK 2 for the⟨ EB⟩ spectrum. Estimates of foreground intensity fluctuations and the nondetection of⟨ BB⟩ and⟨ EB⟩ signals rule out any significant contribution from Galactic foregrounds. The results are consistent with a ΛCDM cosmology seeded by adiabatic perturbations. We note that this is the first detection of CMB polarization …