Deterministic chaos related to a sequence of period-doubling bifurcations (the Feigenbaum transition) has been observed in the NO + CO and NO + H-2 reactions on Pt(100). On a microscopic scale, these reactions are accompanied by the formation of 1x1 adsorbate islands due to the properties of the 1X1 <-> hex phase transition of Pt(100), A simple skeleton model is constructed that describes the behavior of a population of reacting islands which are globally coupled together via the gas phase, Investigations of this model show that the experimentally observed chaotic behavior can result from delays in the response of the reacting islands to partial pressure variations in the gas phase.