Mechanisms enabling genetically identical cells to differentially regulate gene expression are complex and central to organismal development and evolution. While gene silencing pathways involving DNA sequence-specific recruitment of histone-modifying enzymes are prevalent in nature, examples of sequence-independent heritable gene silencing are scarce. Studies of the fission yeast Schizosaccharomyces pombe indicate that sequence-independent propagation of heterochromatin can occur but requires numerous multisubunit protein complexes and their diverse activities. Such complexity has so far precluded a coherent articulation of the minimal requirements for heritable gene silencing by conventional in vitro reconstitution approaches. Here, we take an unconventional approach to defining these requirements by engineering sequence-independent silent chromatin inheritance in budding yeast Saccharomyces cerevisiae cells. The mechanism conferring memory upon these cells is remarkably simple and requires only two proteins, one that recognizes histone H3 lysine 9 methylation (H3K9me) and catalyzes the deacetylation of histone H4 lysine 16 (H4K16), and another that recognizes deacetylated H4K16 and catalyzes H3K9me. Together, these bilingual "read-write" proteins form an interdependent positive feedback loop that is sufficient for the transmission of DNA sequence-independent silent information over multiple generations.