We report the first experimental demonstration of a laser-driven circularly polarized soft-x-ray laser chain. It has been achieved by seeding a 32.8 nm Kr ix plasma amplifier with a high-order harmonic beam, which has been circularly polarized using a four-reflector polarizer. Our measurements testify that the amplified radiation maintains the initial polarization of the seed pulse in good agreement with our Maxwell-Bloch modeling. The resulting fully circular soft-x-ray laser beam exhibits a Gaussian profile and yields about 10^{10} photons per shot, fulfilling the requirements for laboratory-scale photon-demanding application experiments.