The authors report the first realization of a single bosonic Josephson junction using two weakly linked Bose-Einstein condensates in a double-well potential. They investigate the nonlinear tunneling dynamics by measuring the density distribution and deducing the evolution of the relative phase between the two condensates. The results verify the predicted nonlinear generalization of tunneling oscillations and confirm macroscopic quantum self-trapping, where large amplitude tunneling oscillations are inhibited. The experiment allows direct observation of the density distribution and relative phase, revealing distinct dynamical regimes: Josephson oscillations for initial population differences below the self-trapping threshold, and self-trapping for differences above the threshold. The experimental findings are quantitatively consistent with numerical simulations, providing a new tool for studying interacting matter waves in quantum optics.The authors report the first realization of a single bosonic Josephson junction using two weakly linked Bose-Einstein condensates in a double-well potential. They investigate the nonlinear tunneling dynamics by measuring the density distribution and deducing the evolution of the relative phase between the two condensates. The results verify the predicted nonlinear generalization of tunneling oscillations and confirm macroscopic quantum self-trapping, where large amplitude tunneling oscillations are inhibited. The experiment allows direct observation of the density distribution and relative phase, revealing distinct dynamical regimes: Josephson oscillations for initial population differences below the self-trapping threshold, and self-trapping for differences above the threshold. The experimental findings are quantitatively consistent with numerical simulations, providing a new tool for studying interacting matter waves in quantum optics.