By combining the constraints of charge symmetry with new chiral extrapolation techniques and recent low mass lattice QCD simulations of the individual quark contributions to the magnetic moments of the nucleon octet, we obtain a precise determination of the strange magnetic moment of the proton. The result, namely G"s_M = -0.051 #+-# 0.021 #mu#_N, is consistent with the latest experimental measurements but an order of magnitude more precise. This poses a tremendous challenge for future experiments. (orig.)Available from TIB Hannover: RA 8919(04-075) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman