Let　G　be　a　(molecule)　graph.　A　perfect　matching,　or　Kekul,　structure　of　G　is　a　set　of　independent　edges　covering　every　vertex　exactly　once.　Enumeration　of　Kekul,　structures　of　a　graph　is　interest　in　chemistry,　physics　and　mathematics.　In　this　paper,　we　focus　on　the　number　of　perfect　matchings　in　polyomino　chain　graphs.　Simple　exact　formulas　are　given　for　the　expected　value　of　the　number　of　perfect　matchings　in　random　polyomino　chain　graphs　and　for　the　asymptotic　behavior　of　this　expectation.　Moreover,　the　average　value　of　the　number　of　perfect　matchings　with　respect　to　the　set　of　all　polyomino　chain　graphs　with　s　square-cells.