Nucleosome-depleted regions (NDRs) at gene promoters support initiation of RNA polymerase II transcription. Interestingly, transcription often initiates in both directions, resulting in an mRNA and a divergent non-coding (DNC) transcript of unclear purpose. Here, we characterized the genetic architecture and molecular mechanism of DNC transcription in budding yeast. Using high-throughput reverse genetic screens based on quantitative single-cell fluorescence measurements, we identified the Hda1 histone deacetylase complex (Hda1C) as a repressor of DNC transcription. Nascent transcription profiling showed a genome-wide role of Hda1C in repression of DNC transcription. Live-cell imaging of transcription revealed that mutations in the Hda3 subunit increased the frequency of DNC transcription. Hda1C contributed to decreased acetylation of histone H3 in DNC transcription regions, supporting DNC transcription repression by histone deacetylation. Our data support the interpretation that DNC transcription results as a consequence of the NDR-based architecture of eukaryotic promoters, but that it is governed by locus-specific repression to maintain genome fidelity.