Multivalent interactions between effector proteins and histone post-translational modifications are an elementary mechanism of dynamic chromatin signalling. Here we elucidate the mechanism how heterochromatin protein 1α (HP1α), a multivalent effector, is efficiently recruited to the silent chromatin state (marked by trimethylated H3 at Lys9, H3K9me3) while remaining highly dynamic. Employing chemically defined nucleosome arrays together with single-molecule total internal reflection fluorescence microscopy (smTIRFM), we demonstrate that the HP1α residence time on chromatin depends on the density of H3K9me3, as dissociated factors can rapidly rebind at neighbouring sites. Moreover, by chemically controlling HP1α dimerization we find that effector multivalency prolongs chromatin retention and, importantly, accelerates the association rate. This effect results from increased avidity together with strengthened nonspecific chromatin interactions of dimeric HP1α. We propose that accelerated chromatin binding is a key feature of effector multivalency, allowing for fast and efficient competition for binding sites in the crowded nuclear compartment.