The histone modification H3K27me3 plays a central role in Polycomb-mediated epigenetic silencing. H3K27me3 recruits and allosterically activates Polycomb Repressive Complex 2 (PRC2), which adds this modification to nearby histones, providing a read/write mechanism for inheritance through DNA replication. However, for some PRC2 targets, a purely histone-based system for epigenetic inheritance may be insufficient. We address this issue at the Polycomb target FLOWERING LOCUS C (FLC) in Arabidopsis thaliana, as a narrow nucleation region of only ~three nucleosomes within FLC mediates epigenetic state switching and subsequent memory over many cell cycles. To explain the memorys unexpected persistence, we introduce a mathematical model incorporating extra protein memory storage elements with positive feedback that persist at the locus through DNA replication, in addition to histone modifications. Our hybrid model explains many features of epigenetic switching/memory at FLC and encapsulates generic mechanisms that may be widely applicable.