By combining three mutually immiscible polymeric components in a mixed-arm star block terpolymer architecture, we have observed the formation of a previously unknown class of multicompartment micelles in dilute aqueous solution. Connection of water-soluble poly(ethylene oxide) and two hydrophobic but immiscible components (a polymeric hydrocarbon and a perfluorinated polyether) at a common junction leads to molecular frustration when dispersed in aqueous solution. The incompatible hydrophobic blocks form cores that are protected from the water by the poly(ethylene oxide) blocks, but both are forced to make contact with the poly(ethylene oxide) by virtue of the chain architecture. The structures that emerge depend on the relative lengths of the blocks and can be tuned from discrete multicompartment micelles to extended wormlike structures with segmented cores.