Frank-Kasper phases and liquid quasicrystals self-organize from supramolecular spheres of dendrimers, block copolymers, surfactants and other self-assembling molecules. These spheres are expected to be achiral due to their isotropic shape. Nevertheless, supramolecular spheres from short helical stacks of crown like dendrimers self-organize a Pm (3) over barn cubic (Frank-Kasper A15) phase which exhibits chirality on the macroscopic scale. However, the chirality of classic isotropic supramolecular micellar-like spheres, generated from conical dendrons, is unknown. Here we report a library of second and third generation biphenylpropyl dendrons with chiral groups at their apex that produces single-handed chiral supramolecular spheres. Up to 480 conical dendrons self-assemble to form micellar-like spheres, with a molar mass of up to 1.1 x 10(6) g/mol, that self-organize into a Pm (3) over barn phase with chirality detectable on the macroscopic scale. This demonstration of chirality in micellar-like spheres of a Frank-Kasper phase raises the fundamental question whether micellarlike spheres forming 3D phases generated from other soft matter such as block copolymers, surfactants, and other molecules are chiral.