A cell-free massive multiple-input multiple-output system with non-orthogonal multiple-access (NOMA) is investigated. An achievable sum rate is derived and compared against the orthogonal multiple access (OMA) counterpart. Thereby, the detrimental effects of intra-cluster pilot contamination, inter-cluster interference and imperfect successive interference cancellation (SIC) are investigated. The number of users served simultaneously by NOMA can be significantly higher than that of OMA. Nevertheless, the achievable sum rate of NOMA can be lower than that of OMA even in the regime of low number of users due to intra-cluster pilot contamination and error propagation of imperfect SIC.