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In this paper, we aim to design an adaptive power allocation scheme to minimize the average transmit power of a hybrid automatic repeat request with chase combining (HARQ-CC) enabled non-orthogonal multiple access (NOMA) system under strict outage constraints of users. Specifically, we assume the base station only knows the statistical channel state information of the users. We first focus on the two-user cases. To evaluate the performance of the two-user HARQ-CC enabled NOMA systems, we first analyze the outage probability of each user. Then, an average power minimization problem is formulated. However, the attained expressions of the outage probabilities are nonconvex, and thus make the problem difficult to solve. Thus, we first conservatively approximate it by a tractable one and then use a successive convex approximation based algorithm to handle the relaxed problem iteratively. For more practical applications, we also investigate the HARQ-CC enabled transmissions in multi-user scenarios. The user-paring and power allocation problem is considered. With the aid of matching theory, a low complexity algorithm is presented to first handle the user-paring problem. Then the power allocation problem is solved by the proposed SCA-based algorithm. Simulation results show the efficiency of the proposed transmission strategy and the near-optimality of the proposed algorithms.