Nucleosomes, the structural building blocks of chromatin, possess 2-fold pseudo symmetry which can be broken through differential modification or removal of one copy of a pair of sister histones. The resultant asymmetric nucleosomes and hexasomes have been implicated in gene regulation, yet the use of these noncanonical substrates in chromatin biochemistry is limited, owing to the lack of efficient methods for their preparation. Here, we report a strategy that allows the orientation of these asymmetric species to be tightly controlled relative to the underlying DNA sequence. Our approach is based on the use of truncated DNA templates to assemble oriented hexasomes followed by DNA ligation and, in the case of asymmetric nucleosomes, addition of the missing heterotypic histones. We show that this approach is compatible with multiple nucleosome positioning sequences, allowing the generation of desymmetrized mononucleosomes and oligonucleosomes with varied DNA overhangs and heterotypic histone H2A/H2B dimer compositions. Using this technology, we examine the functional consequences of asymmetry on BRG1/BRM associated factor (BAF) complex-mediated chromatin remodeling. Our results indicate that cancer-associated histone mutations can reprogram the inherent activity of BAF chromatin remodeling to induce aberrant chromatin structure.