A self-aligning stacked memory cell array structure and method for fabricating such structure. The memory cell array includes a stack of memory cells disposed adjacent to opposing sides of a conductive line that is formed within a trench. The memory cells are stacked such that the memory element surface of each memory cell forms a portion of the sidewall of the conductive line. The conductive line is formed within the trench such that electrical contact is made across the entire memory element surface of each memory cell. Such structure and method for making such structure is a self-aligning process that does not require the use of any additional masks.