Treatment with histone deacetylase inhibitors (HDACI) results in potent cytotoxicity of a variety of cancer cell types, and these drugs are used clinically to treat hematological tumors. They are known to repress the transcription of ERBB2 and many other oncogenes, but little is known about this mechanism. Using global run-on sequencing (GRO-seq) to measure nascent transcription, we find that HDACI cause transcriptional repression by blocking RNA polymerase II elongation. Our data show that HDACI preferentially repress the transcription of highly expressed genes as well as high copy number genes in HER2+ breast cancer genomes. In contrast, genes that are activated by HDACI are moderately expressed. We analyzed gene copy number in combination with microarray and GRO-seq analysis of expression level, in normal and breast cancer cells to show that high copy number genes are more likely to be repressed by HDACI than non-amplified genes. The inhibition of transcription of amplified oncogenes, which promote survival and proliferation of cancer cells, might explain the cancer-specific lethality of HDACI, and may represent a general therapeutic strategy for cancer.