A novel hybrid organic/inorganic triblock copolymer of polystyrene-butadiene-polystyrene (SBS) containing grafted polyhedral oligomeric silsesquioxane (POSS) molecules was synthesized by a hydrosilation method. The POSS molecules were designed to contain a single silane functional group, which was used to graft onto the dangling 1,2-butadienes in the polybutadiene soft block. Unlike typical free radical copolymerizations commonly used for many other POSS incorporations investigated, this synthesis method allows us to make a series of polymers with varying amounts of POSS without any change to the overall degree of polymerization or structure of the main SBS backbone. This gives us a unique opportunity to study the POSS behavior in the matrix and know that all differences are solely due to the POSS grafted to the soft continuous butadiene phase. X-ray diffraction revealed that the grafted POSS are very well dispersed in the matrix of the hybrid polymer, which is compared to the strong phase segregation observed in a POSS physical blend. Small-angle X-ray scattering indicates that although the cylindrical morphology attributed to the styrene component was not altered by the presence of POSS, attachment of POSS to the continuous phase (polybutadiene block) causes the packing of discrete phase (polystyrene blocks) to lack long-range features. Results of dynamic mechanical analysis showed that the POSS has sterically hindered the motion of the polybutadiene blocks. More interestingly, the presence of POSS in the soft segments also resulted in a tapered tan delta peak associated with the glass transition of polystyrene and a higher tensile strength when deformed at temperature near T-g of polystyrene without affecting the elongational behavior of SBS at temperatures above T-g of polybutadiene.