Intellectual disability is a well-known hallmark of Down Syndrome (DS) that results from the triplication of the critical region of human chromosome 21 (HSA21). Major studies were conducted in recent years to gain an understanding about the contribution of individual triplicated genes to DS-related brain pathology. Global transcriptomic alterations and widespread changes in the establishment of neural lineages, as well as their differentiation and functional maturity, suggest genome-wide chromatin organization alterations in trisomy. High Mobility Group Nucleosome Binding Domain 1 (HMGN1), expressed from HSA21, is a chromatin remodeling protein that facilitates chromatin decompaction and is associated with acetylated lysine 27 on histone H3 (H3K27ac), a mark correlated with active transcription. Recent studies causatively linked overexpression of HMGN1 in trisomy and the development of DS-associated B cell acute lymphoblastic leukemia (B-ALL). HMGN1 has been shown to antagonize the activity of the Polycomb Repressive Complex 2 (PRC2) and prevent the deposition of histone H3 lysine 27 trimethylation mark (H3K27me3), which is associated with transcriptional repression and gene silencing. However, the possible ramifications of the increased levels of HMGN1 through the derepression of PRC2 target genes on brain cell pathology have not gained attention. In this review, we discuss the functional significance of HMGN1 in brain development and summarize accumulating reports about the essential role of PRC2 in the development of the neural system. Mechanistic understanding of how overexpression of HMGN1 may contribute to aberrant brain cell phenotypes in DS, such as altered proliferation of neural progenitors, abnormal cortical architecture, diminished myelination, neurodegeneration, and Alzheimer’s disease-related pathology in trisomy 21, will facilitate the development of DS therapeutic approaches targeting chromatin.