Irregular repetition slotted aloha (IRSA) is a massive random access protocol which can be used to serve a large number of users while achieving a packet loss rate (PLR) close to zero. However, if the number of users is too high, then the system is interference limited and the PLR is close to one. In this paper, we propose a variant of IRSA in the interference limited regime, namely Censored-IRSA (C-IRSA), wherein users with poor channel states censor themselves from transmitting their packets. We theoretically analyze the throughput performance of C-IRSA via density evolution. Using this, we derive closed-form expressions for the optimal choice of the censor threshold which maximizes the throughput while achieving zero PLR among uncensored users. Through extensive numerical simulations, we show that C-IRSA can achieve a 4$\times$ improvement in the peak throughput compared to conventional IRSA.