The five enigmatic cocoon stars, after which the Quintuplet cluster was christened, have puzzled astronomers since their discovery. Their extraordinary cool, featureless thermal spectra have been attributed to various stellar types from young to highly evolved, whereas their absolute luminosities place them among the supergiants. We present diffraction-limited images from the Keck 1 telescope that resolve this debate with the identification of rotating spiral plumes characteristic of colliding-wind binary "pinwheel" nebulae. Such elegant spiral structures, found around high-luminosity Wolf-Rayet stars, have recently been implicated in the behavior of supernovae light curves in the radio and optical.