A 2D cocrystal that displays random mixing along one axis and periodic ordering along the other axis is discovered. The characteristics and formation process of this "1D-cocrystal" are examined with atomic detail by scanning tunneling microscopy (STM) at the liquid/solid interface and through computed models. This type of cocrystallization causes an alignment shift to satisfy close packing. The frequency of the alignment shift can be controlled by variation of the ratio of adsorbates in solution. Furthermore, a reversible monolayer reorganization induced through perturbing the STM bias voltage provides not only mechanistic insights into the formation process of the 1D-cocrystal but also the potential for applications as a molecular switch. The control over surface composition and periodicity by controlling the molar ratio of components offers an unexploited approach to nanoscale patterning.