We report As-75 nuclear magnetic resonance studies on an underdoped single-crystal Ba0.77K0.23Fe2As2 with T-c = 16.5 K. Below T-N = 46 K, the NMR peaks for H parallel to c split and those for H parallel to a shift to higher frequencies, which indicates that an internal magnetic field along the c axis develops below T-N. The spin-lattice relaxation rate 1/T-1 measured at the shifted peak with H parallel to a, which experiences the internal field, shows a distinct decrease below T-c(mu H-0 = 12 T) = 16 K, following a T-3 relation at low temperatures. Our results show unambiguously that antiferromagnetic order and superconductivity coexist microscopically. The unusual superconducting state with the coexisting magnetism is highlighted.