This paper is the first report of electrospinning neat polyisobutylene-based thermoplastic elastomers. Two generations of these materials are investigated: a linear poly(styrene-b-isobutylene-b-styrene) (L_SIBS) triblock copolymer and a dendritic poly(isobutylene-b-p-methylstyrene) (D_IB-MS), also a candidate for biomedical applications. Cross-polarized optical microscopy shows birefringence, indicating orientation in the electrospun fibers, which undergo large elongation and shear during electrospinning. In contrast to the circular cross section of L_SIBS fibers, D_IB-MS yields dumbbell-shaped fiber cross sections for the combination of processing conditions, molecular weight, and architecture. Hydrophobic surfaces with a water contact angle as high as 146 +/- 30 degrees were obtained with D_IB-MS that had the noncircular fiber cross section and a hierarchical arrangement of nano-to micrometer-sized fibers in the mat. These highly water repellent fiber mats were found to serve as an excellent scaffold for bovine chondrocytes to produce cartilage tissue.