We study a class of dark matter models in which the dark matter is a baryon-like composite particle of a confining gauge group and also a pseudo-Nambu-Goldstone boson associated with the breaking of an enhanced chiral symmetry group. The approximate symmetry decouples the dark matter mass from the confinement scale of the new gauge group, leading to correct thermal relic abundances for dark matter masses far below the unitary bound, avoiding the typical conclusion of thermally produced composite dark matter. We explore the available parameter space in a minimal example model based on an SU(2) gauge group, and discuss prospects for experimental detection.