The monolayer structure of CO molecules adsorbed on MgO(100) single crystal surfaces cleaved in situ has been analysed by LEED within the 30-56 K temperature range. At T less-than-or-equal-to 40 K CO forms a 2 x 4 commensurate 2D solid phase. A sharp uniaxial transition occurs above this temperature, along the [10] surface direction which locks the monolayer into a new commensurate 2 x 3 phase stable over a temperature range of 8 K. Above 50 K, this second commensurate phase expands itself uniaxially in a sharp transition toward a solid with disorder increasing with temperature. This succession of transitions is an interesting illustration of the incomplete "devil's staircase".