A precise measurement of the analyzing power AN in proton–proton elastic scattering in the region of 4-momentum transfer squared 0.001 < |t | < 0.032 (GeV/c)2 has been performed using a polarized atomic hydrogen gas jet target and the 100 GeV/c RHIC proton beam. The interference of the electromagnetic spin-flip amplitude with a hadronic spin-nonflip amplitude is predicted to generate a significant AN of 4–5%, peaking at −t 0.003 (GeV/c)2. This kinematic region is known as the Coulomb nuclear interference region. A possible hadronic spin-flip amplitude modifies this calculable prediction. We present the first precise result of the CNI asymmetry and shape as a function of t . Our data are well described by the CNI prediction with the electromagnetic spin-flip alone and do not support the presence of a large hadronic spin-flip amplitude. © 2006 Elsevier B.V. PACS: 13.88.+e; 13.85.Dz; 29.25.Pj