High-throughput chemical screens typically use coarse assays such as cell survival, limiting what can be learned about mechanisms of action, off-target effects, and heterogeneous responses. Here, we introduce "sci-Plex," which uses "nuclear hashing" to quantify global transcriptional responses to thousands of independent perturbations at single-cell resolution. As a proof of concept, we applied sci-Plex to screen three cancer cell lines exposed to 188 compounds. In total, we profiled similar to 650,000 single-cell transcriptomes across similar to 5000 independent samples in one experiment. Our results reveal substantial intercellular heterogeneity in response to specific compounds, commonalities in response to families of compounds, and insight into differential properties within families. In particular, our results with histone deacetylase inhibitors support the view that chromatin acts as an important reservoir of acetate in cancer cells.