Surface tension measurements reveal surface freezing in liquid n-alkanes. A solid monolayer of molecules is found to exist up to 30 degrees C above the bulk freezing point. This surface phase exists only for carbon numbers 14 n </= 50. The measured carbon number and temperature dependence of the surface tension is interpreted within a simple thermodynamical model based on known bulk latent heat data and surface energy considerations. The vanishing of the surface phase for n </= 14 is a possible transition from surface freezing to surface melting behavior.