  Despite their technological relevance, a full microscopic understanding of
glasses is still lacking. This applies even more to their surfaces whose
properties largely differ from that of the bulk material. Here, we
experimentally investigate the surface of a two-dimensional glass as a function
of the effective temperature. To yield a free surface, we use an attractive
colloidal suspension of micron-sized particles interacting via tunable critical
Casimir forces. Similar to crystals, we observe surface melting of the glass,
i.e., the formation of a liquid film at the surface well below the glass
temperature. Underneath, however, we find an unexpected region with bulk
density but much faster particle dynamics. It results from connected clusters
of highly mobile particles which are formed near the surface and deeply
percolate into the underlying material. Because its thickness can reach several
tens of particle diameters, this layer may elucidate the poorly understood
properties of thin glassy films which find use in many technical applications
