In a quantum anomalous Hall insulator coupled to an s-wave superconductor, the surface Dirac fermion at the interface forms a px+ipy type of superconductor, which can accommodate one-dimensional chiral Majorana fermion modes propagating along the edges when the topological order is carefully controlled. Experimental signatures of this mode is captured by the magneto-electric transport measurements in a hybrid system of a quantum anomalous Hall insulator [Cr-doped (Bi,Sb)2Te3] thin film partially capped by a superconductor layer (Nb). The external magnetic field serves as a “knob” to tune the system into different topological regimes that allow the degenerate and non-degenerate propagation of Majorana edge modes. This tuning was signified as quantized conductance transitions among e2/h, 0.5e2/h, and 0 as the external magnetic field was swept, during which the conductance quantized at 0.5e2/h is the hallmark of the single chiral Majorana fermion phase. This transport signature is reproducible over many magnetic field sweeps and appears at different temperatures, providing a solid signature of the chiral Majorana fermion modes.