HIV-1 eradication strategies require complete reactivation of HIV-1 latent cells by Latency Reversing Agents (LRA). Current methods lack effectiveness due to incomplete proviral reactivation. We employed a single-molecule RNA-FISH (smRNA-FISH) and FISH-Quant analysis and found that proviral reactivation is highly variable from cell-to-cell, stochastic, and occurs in bursts and waves, with different kinetics in response to diverse LRAs. Approximately 1-5% of latent cells exhibited stochastic reactivation without LRAs. Through single-cell RNA-seq analysis, we identified NR4A3 and cMYC as extrinsic factors associated with stochastic HIV-1 reactivation. Concomitant with HIV-1 reactivation cMYC was downregulated and NR4A3 was upregulated in both latent cell lines and primary CD4+ T-cells from aviremic patients. By inhibiting cMYC using SN-38, an active metabolite of irinotecan, we induced NR4A3 and HIV-1 expression. Our results suggest that inherent stochasticity in proviral reactivation contributes to cell-to-cell variability, which could potentially be modulated by drugs targeting cMYC and NR4A3.