This paper describes a detailed investigation of the structure of butyl rubber by one- and two-dimensional NMR methods. Butyl rubber is a copolymer of isobutylene with 1-3 mol % isoprene and is prepared by cationic polymerization. Our goal was to determine secondary methods of isoprene incorporation other than 1,4-addition. Possibilities include 1,2-, 3,4-, or 4,3-addition. We found no evidence for structure arising from either of these possibilities, although there have been previous reports of 1,2-addition in the literature. We present the first identification of a second type of structure, however, which is a branch point in the polymer chain. This minor structure presumably results from 1,4-addition followed by rearrangement and subsequent isobutylene addition to form the branch point. The minor structure is present in both commercial butyl materials and laboratory isobutylene/isoprene copolymers polymerized at various temperatures. The amount of the minor branched isoprene species increases relative to the 1,4-addition product with increasing polymerization temperature. We discuss GPC and rheological data which suggest that the branch point detected by NMR is associated with long-chain branches.