The time-resolved production of HO2 in the Cl-initiated oxidation of iso- and n-butane is measured using continuous-wave (CW) infrared frequency modulation spectroscopy between 298 and 693 K. The yield of HO2 is determined relative to the Cl2/CH3OH/O2 system. As in studies of smaller alkanes, the branching fraction to HO2 + alkene in butyl + O2 displays a dramatic rise with increasing temperature between about 550 and 700 K (the "transition region") which is accompanied by a qualitative change in the time behavior of the HO2 production. At low temperatures the HO2 is formed promptly; a second, slower production of HO2 is responsible for the bulk of the increased yield in the transition temperature region. In contrast to reactions of smaller alkyl radicals with O2, the total HO2 yield in the butyl radical reactions appears to remain significantly below 1 up to 700 K, implying a significant role for OH-producing channels. The slower HO2 production in butane oxidation displays an apparent activation energy similar to that measured for smaller alkyl + O2 reactions, suggesting that the energetics of the HO2 elimination transition state are similar for a broad range of R + O2 systems. A combination of QCISD(T) based characterizations of the propyl and butyl + O2 potential energy surfaces and master equation based characterization of the propyl + O2 kinetics provide the framework for explanation of the experimentally observed HO2 production in Cl-initiated propane and butane oxidation. These calculations suggest that the HO2 elimination channel is similar in all reaction systems, and that hydroperoxyalkyl (QOOH) species produced by internal H-atom abstraction in RO2 can provide a path to OH formation. However, the QOOH formed by the energetically favorable 1,5 isomerization (via a six-membered ring transition state) generally experiences significant barriers (relative to the radical + O2 reactants) to the production of an oxetane + OH. In contrast, the barriers to forming OH + an oxirane or an oxolane, via 1,4 or 1,6 isomerizations, respectively, are generally below reactants.