Cool flames accompanying the spontaneous combustion of, gaseous hydrocarbon fuels are a familiar manifestation of oscillatory chemical reactions in combustion systems. The possibility of oscillatory instability is of importance technically, as well as of general interest, and its consequence can be as significant as those of ignition and extinction. Clear experimental tests of theoretical predictions for the onset and growth of oscillations have, been complicated by the intricate kinetic mechanism involved. Complex kinetics is not, however, a necessary pre-requisite for oscillations. We have devised, and realized experimentally, the simplest thermokinetic oscillator in a well-stirred closed vessel (semi-batch reactor) by adaptation of a scheme suggested by Salnikov. Only one chemical reaction occurs and this is a first-order step. Reaction is exothermic and operates under non-isothermal, non-adiabatic conditions. The novel technique employed here is that of a slow, controlled entry of the reactants via a calibrated capillary rather than the usual rapid admission. The reaction exothermicity is an important parameter determining the existence of oscillations and can be tuned as required, without altering the reaction kinetics, by the addition of oxygen. The conditions for the onset and growth of oscillatory responses are predicted analytically on the basis of a simple model. The system allows the quantitative identification of the required relative magnitudes of the characteristics timescales for chemical reaction and Newtonian heat transfer. The ramifications of these results for the combustion of hydrocarbons where there is an inseparable coupling of both thermal and chemical feedback is discussed.