Condensed matter textbooks teach us that melting cannot be continuous and indeed experience, including with polymers and other long-chain compounds, tells us that it is a strongly first-order transition. However, here we report nearly continuous melting of monolayers of ultralong n-alkane C390H782 on graphite, observed by AFM and reproduced by mean-field theory and MD simulation. On heating, the crystal-melt interface moves steadily and reversibly from chain ends inward. Remarkably, the final melting point is 80 K above that of the bulk, and equilibrium crystallinity decreases continuously from ~100% to <50% prior to final melting. We show that the similarity in melting behavior of polymers and non-polymers is coincidental. In the bulk, the intermediate melting stages of long-chain crystals are forbidden by steric overcrowding at the crystal-liquid interface. However, there is no crowding in a monolayer as chain segments can escape to the third dimension.