The eukaryotic genome is divided into functional domains defined in part by local differences in chromatin structure and delimited in many cases by boundary elements. The HML and HMR loci in the yeast Saccharomyces cerevisiae are transcriptionally silent chromosome domains. Each locus is bracketed by two cis-acting sequences, designated E and I, that serve to establish and maintain repression of genes within each locus. We show that repression at HML is uniformly high between E and I but decreases sharply beyond I. The region of repression at HML generally correlates with the domain of histone hypoacetylation. Despite the sharp definition of the boundaries of HML, no sequence capable of blocking the spread of heterochromatin resides in the sequences flanking HML. We find, though, that inverting the orientation of I increases silencing outside of HML while weakening silencing within HML. These results indicate that the HML I silencer establishes a boundary between active and inactive chromatin at HML, but does so by organizing inactive chromatin in only one direction. This represents a different mechanism for delimiting the boundaries of a eukaryotic chromosome domain.