The combination between non-orthogonal multiple access (NOMA) and hybrid automatic repeat request (HARQ) is capable of realizing ultra-reliability, high throughput and massive concurrent connections particularly for emerging communication systems. This paper focuses on characterizing the asymptotic scaling law of the outage probability of the HARQ with chase combining (HARQ-CC)-aided downlink NOMA scheme with respect to the transmit power, i.e., diversity order. The diversity order of the two- user HARQ-CC-aided NOMA system is derived in closed-form, where an integration domain partition trick is developed to obtain the upper and lower bounds of the outage probability. The analytical results show that the diversity order is a decreasing step function of transmission rate given the ratio between the transmit powers allocated to the two users. Moreover, full time diversity can only be achieved under a sufficiently low transmission rate. Additionally, the users' diversity orders follow a descending order according to their respective average channel gains. Monte Carlo simulations finally confirm the analysis.