Giant random telegraph noise (RTN) in the resistance fluctuation of a macroscopic film of perovskite-type manganese oxide La(2/3)Ca(1/3)MnO3 has been observed at various temperatures ranging from 4 to 170 K, well below the Curie temperature ( T(C) approximately 210 K). The amplitudes of the two-level fluctuations vary from 0.01% to 0.2%. We discuss the origin of the RTN to be a dynamic mixed-phase percolative conduction process, where manganese clusters switch back and forth between two phases that differ in their conductivity and magnetization.