The oxidation of ultra-thin Mg layers deposited on a clean Ag(111) surface was investigated at room temperature by means of scanning tunneling microscopy (STM). Long-range organized MgO surfaces could be obtained, all of them showing atomically smooth one-dimensional lines with elementary dots inside. These dotted lines with an apparent width of 1 or 2.5nm most often run parallel and rotated by about 30° with respect to a Ag close-packed axis. The three-fold symmetry in the dot arrangement and the measured apparent heights are consistent with polar-orientated MgO(111) layers. Two dot periodicities are observed, whose origin is attributed to coincidence lattices between silver and a 30° rotated hexagonal MgO layer.