This paper focuses on the development of intelligent reflection surface (IRS) assisted non-orthogonal multiple access (NOMA), where the hybrid automatic repeat request with chase combining (HARQ-CC) is exploited to improve the system's reliability. We first investigate the outage behavior of HARQ-CC-assisted IRS-NOMA, where the exact and asymptotic closed-from expressions of the outage probability of a pair of users are derived. Based on the asymptotic outage probability, the diversity order of a pair of users for HARQ-CC-assisted IRS-NOMA is obtained, and it is in connection with the number of reflection elements and the number of transmission rounds. The numerical results are shown to substantiate the accuracy of the derived analytical results and demonstrate that: 1) The HARQ-CC-assisted IRS-NOMA systems can achieve a significant performance gain compared with the IRS-NOMA systems; 2) The HARQ-CC-assisted IRS-NOMA system outperforms the HARQ-CC-assisted IRS-OMA system in terms of outage probability and diversity order.