The chromatin landscape of DNA and histone modifications represents a fundamental layer of cellular regulation. These modifications, which are implicated in gene regulation and even complex properties such as epigenetic programs, allow eukaryotic organisms to expand information content beyond DNA sequence. Despite its rich regulatory potential, our ability to manipulate this landscape in living cells remains limited. Here we exploit DNA adenine methylation (m6A), a modification rarely found in metazoan genomes, to construct a fully synthetic chromatin system in human cells. Our system is composed of three functional modules that mediate m6A operations: (1) synthetic initiator module to place m6A at specific genomic sites; (2) synthetic readout module to recognize m6A and mediate m6A-dependent transcriptional logic; (3) propagation module that implements “read-write”, a mechanism proposed to underlie chromatin spreading and epigenetic maintenance across cellular systems. Together with a quantitative model, we combine these modules to construct regulatory circuits that drive spatial m6A propagation to regulate distal genes, and enable epigenetic memory of transcriptional states. These epigenetic functions are engineered de novo and do not make use of endogenous mechanisms, providing evidence that complex behaviors like memory can be programmed using specific molecular mechanisms at the chromatin level. Our work establishes a synthetic, chromatin ‘programming language’ to expand the regulatory potential of the genome and engineer epigenetic functions in mammalian cells.