The field responsible for the cosmological curvature perturbations generated during a stage of primordial inflation might be the ``curvaton'', a field different from the inflaton field. To keep the effective mass of the curvaton small enough compared to the Hubble rate during inflation one may not invoke supersymmetry since the latter is broken by the vacuum energy density. In this paper we propose the idea that the curvaton is a pseudo Nambu-Goldstone boson (PNGB) so that its potential and mass vanish in the limit of unbroken symmetry. We give a general framework within which PNGB curvaton candidates should be explored. Then we explore various possibilities, including the case where the curvaton can be identified with the extra-component of a gauge field in a compactified five-dimensional theory (a Wilson line), where it comes from a Little-Higgs mechanism, and where it is a string axion so that supersymmetry is essential.