We report the first observation of the multilayer band splitting in the optimally doped trilayer cuprate Bi2Sr2Ca2Cu3O(10+δ) (Bi2223) by angle-resolved photoemission spectroscopy. The observed energy bands and Fermi surfaces are originated from the outer and inner CuO2 planes (OP and IP). The OP band is overdoped with a large d-wave gap around the node of Δ0∼43 meV while the IP is underdoped with an even large gap of Δ0∼60 meV. These energy gaps are much larger than those for the same doping level of the double-layer cuprates, which leads to the large Tc in Bi2223. We propose possible origins of the large superconducting gaps for the OP and IP: (1) minimal influence of out-of-plane disorder and a proximity effect and (2) interlayer tunneling of Cooper pairs between the OP and IP.