The existence of coherent magnetic correlations in the normal phase of cuprate high-temperature superconductors has proven difficult to measure directly. Here we report on a study of ferromagnetic-superconductor bilayers of La 2/3Ca 1/3MnO 3/YBa 2Cu 3O 7 (LCMO/YBCO) with varying YBCO layer thicknesses. Using x-ray magnetic circular dichroism, we demonstrate that the ferromagnetic layer induces a Cu magnetic moment in the adjacent high-temperature superconductor. For thin samples, this moment exists at all temperatures below the Curie temperature of the LCMO layer. However, for a YBCO layer thicker than 12 unit cells, the Cu moment is suppressed for temperatures above the superconducting transition, suggesting this to be a direct measurement of magnetic coherence in the normal state of a superconducting oxide.