a log del pezzo surface is a normal log terminal surface with anti-ample canonical bundle. over the complex numbers, keel and mckernan have classified all but a bounded family of the simply connected log del pezzo surfaces of rank one. in this talk we extend their classification in positive characteristic, and in particular we prove that for $p>5$ every log del pezzo surface of rank one lifts to characteristic zero with smooth base. as a consequence, we see that kawamata-viehweg vanishing holds in this setting. finally, we exhibit some counter-examples in characteristic two, three and five.