A general approach for heritably altering gene expression has the potential to enable many discovery and therapeutic efforts. Here, we present CRISPRoff-a programmable epigenetic memory writer consisting of a single dead Cas9 fusion protein that establishes DNA methylation and repressive histone modifications. Transient CRISPRoff expression initiates highly specific DNA methylation and gene repression that is maintained through cell division and differentiation of stem cells to neurons. Pairing CRISPRoff with genome-wide screens and analysis of chromatin marks establishes rules for heritable gene silencing. We identify single guide RNAs (sgRNAs) capable of silencing the large majority of genes including those lacking canonical CpG islands (CGIs) and reveal a wide targeting window extending beyond annotated CGIs. The broad ability of CRISPRoff to initiate heritable gene silencing even outside of CGIs expands the canonical model of methylation-based silencing and enables diverse applications including genome-wide screens, multiplexed cell engineering, enhancer silencing, and mechanistic exploration of epigenetic inheritance.