Experiments designed to simulate the low temperature surface chemistry occurring in interstellar clouds provide clear evidence of a reaction between oxygen atoms and propyne ice. The reactants are dosed onto a surface held at a fixed temperature between 14 and 100 K. After the dosing period, temperature programmed desorption (TPD), coupled with time-of-flight mass spectrometry, are used to identify two reaction products with molecular formulae C3H4O and C3H4O2. These products result from the addition of a single oxygen atom, or two oxygen atoms, to a propyne reactant. A simple model has been used to extract kinetic data from the measured yield of the single-addition (C3H4O) product at surface temperatures from 30–100 K. This modelling reveals that the barrier of the solid-state reaction between propyne and a single oxygen atom (160 ± 10 K) is an order of magnitude less than that reported for the gas-phase reaction. In addition, estimates for the desorption energy of propyne and reaction rate coefficient, as a function of temperature, are determined for the single addition process from the modelling. The yield of the single addition product falls as the surface temperature decreases from 50 K to 30K, but rises again as the surface temperature falls below 30 K. This increase in the rate of reaction at low surface temperatures is indicative of an alternative, perhaps barrierless, pathway to the single addition product which is only important at low surface temperatures. The kinetic model has been further developed to characterize the double addition reaction, which appears to involve the addition of a second oxygen atom to C3H4O. This modelling indicates that this second addition is a barrierless process. The kinetic parameters we extract from our experiments indicate that the reaction between atomic oxygen and propyne could occur under on interstellar dust grains on an astrophysical time scale.