This letter analyzes the ergodic rates of a simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) aided non-orthogonal multiple access (NOMA) system, where the direct links from the base station to cell-edge users are non-line-of-sight due to obstacles, and STAR-RIS is used to provide line-of-sight links to these cell-edge users. By fitting the distribution of the composite channel power gain to a gamma distribution, we derive the closed-form expressions of ergodic rates and high signal-to-noise ratio (SNR) slopes for cell-edge users. Numerical results reveal that 1) the ergodic rates increase with the number of STAR-RIS elements, and the high SNR slopes are fixed as constants; 2) STAR-RIS aided NOMA systems achieve higher ergodic rates than conventional RIS aided NOMA systems.