Non-orthogonal Multiple Access (NOMA) has become a salient technology for improving the spectral efficiency of the next generation 5G wireless communication networks. In this paper, the achievable average rate of an Opportunistic Non-Orthogonal Multiple Access (O-NOMA) based Cooperative Relaying System (CRS) is studied under Rician fading channels with Channel State Information (CSI) available at the source terminal. Based on CSI, for opportunistic transmission, the source immediately chooses either the direct transmission or the cooperative NOMA transmission using the relay, which can provide better achievable average rate performance than the existing Conventional-NOMA (C-NOMA) based CRS with no CSI at the source node. Furthermore, a mathematical expression is also derived for the achievable average rate and the results are compared with C-NOMA based CRS with no CSI at the transmitter end, over a range of increasing power allocation coefficients, transmit Signal-to-Noise Ratios (SNRs) and average channel powers. Numerical results show that the CRS using O-NOMA with CSI achieves better spectral efficiency in terms of the achievable average rate than the Conventional-NOMA based CRS without CSI. To check the consistency of the derived analytical results, Monte Carlo simulations are performed which verify that the results are consistent and matched well with the simulation results.