In addition to their annotated transcript, many eukaryotic mRNA promoters produce divergent noncoding transcripts. To define determinants of divergent promoter directionality, we used genomic replacement experiments. Sequences within noncoding transcripts specified their degradation pathways, and functional protein-coding transcripts could be produced in the divergent direction. To screen for mutants affecting the ratio of transcription in each direction, a bidirectional fluorescent protein reporter construct was introduced into the yeast nonessential gene deletion collection. We identified chromatin assembly as an important regulator of divergent transcription. Mutations in the CAF-I complex caused genome-wide derepression of nascent divergent noncoding transcription. In opposition to the CAF-I chromatin assembly pathway, H3K56 hyperacetylation, together with the nucleosome remodeler SWI/SNF, facilitated divergent transcription by promoting rapid nucleosome turnover. We propose that these chromatin-mediated effects control divergent transcription initiation, complementing downstream pathways linked to early termination and degradation of the noncoding RNAs.