The resonantly stabilized radical i-C(4)H(5) (CH(2)CCHCH(2)) is an important intermediate in the combustion of unsaturated hydrocarbons and is thought to be involved in the formation of polycyclic aromatic hydrocarbons through its reaction with acetylene (C(2)H(2)) to form benzene + H. This study uses quantum chemistry and statistical reaction rate theory to investigate the mechanism and kinetics of the i-C(4)H(5) + O(2) reaction as a function of temperature and pressure, and unlike most resonantly stabilized radicals we show that i-C(4)H(5) is consumed relatively rapidly by its reaction with molecular oxygen. O(2) addition occurs at the vinylic and allenic radical sites in i-C(4)H(5), with respective barriers of 0.9 and 4.9 kcal mol(-1). Addition to the allenic radical form produces an allenemethylperoxy radical adduct with only around 20 kcal mol(-1) excess vibrational energy. This adduct can isomerize to the ca. 14 kcal mol(-1) more stable 1,3-divinyl-2-peroxy radical via concerted and stepwise processes, both steps with barriers around 10 kcal mol(-1) below the entrance channel energy. Addition of O(2) to the vinylic radical site in i-C(4)H(5) directly forms the 1,3-divinyl-2-peroxy radical with a small barrier and around 36.8 kcal mol(-1) of excess energy. The 1,3-divinyl-2-peroxy radical isomerizes via ipso addition of the O(2) moiety followed by O atom insertion into the adjacent C-C bond. This process forms an unstable intermediate that ultimately dissociates to give the vinyl radical, formaldehyde, and CO. At higher temperatures formation of vinylacetylene + HO(2), the vinoxyl radical + ketene, and the 1,3-divinyl-2-oxyl radical + O paths have some importance. Because of the adiabatic transition states for O(2) addition, and significant reverse dissociation channels in the peroxy radical adducts, the i-C(4)H(5) + O(2) reaction proceeds to new products with rate constant of around 10(11) cm(3) mol(-1) s(-1) at typical combustion temperatures (1000-2000 K). For fuel-rich flames we show that the reaction of i-C(4)H(5) with O(2) is likely to be faster than that with C(2)H(2), bringing into question the importance of the i-C(4)H(5) + C(2)H(2) reaction in initiating ring formation in sooting flames.