Chromatin architecture is regulated through both enzymatic and non-enzymatic activities. For example, the Polycomb Group (PcG) proteins maintain developmental gene silencing using an array of chromatin-based mechanisms. The essential Drosophila PcG protein, Posterior Sex Combs (PSC), compacts chromatin and inhibits chromatin remodeling and transcription through a non-enzymatic mechanism involving nucleosome bridging. Nucleosome bridging is achieved through a combination of nucleosome binding and self-interaction. Precisely how PSC interacts with chromatin to bridge nucleosomes is not known and is the subject of this work. We determine the stoichiometry of PSC-chromatin interactions in compact chromatin (in which nucleosomes are bridged) using Scanning Transmission Electron Microscopy (STEM). We find that full compaction occurs with one PSC per nucleosome. In addition to compacting chromatin, we show that PSC oligomerizes nucleosome arrays. PSC-mediated oligomerization of chromatin occurs at similar stoichiometry as compaction suggesting it may also involve nucleosome bridging. Interactions between the tail of histone H4 and the acidic patch of histone H2A are important for chromatin folding and oligomerization, and several chromatin proteins bind the histone H2A acidic patch. However, mutation of the acidic patch of histone H2A does not affect PSC's ability to inhibit chromatin remodeling or bridge nucleosomes. In fact, PSC does not require nucleosomes for bridging activity but can bridge naked DNA segments. PSC clusters nucleosomes on sparsely assembled templates, suggesting it interacts preferentially with nucleosomes over bare DNA. This may be due to the ability of PSC to bind free histones. Our data are consistent with a model in which each PSC binds a nucleosome and at least one other PSC to directly bridge nucleosomes and compact chromatin, but also suggest that naked DNA can be included in compacted structures. We discuss how our data highlight the diversity of mechanisms used to modify chromatin architecture.