The transition to a new magnetic topology, characterized by a quasi-single-helicity state with a single helical magnetic axis has been experimentally observed for the first time in a reversed-field-pinch plasma. The occurrence of the new state, which has been dubbed a single-helical-axis state, was found to provide magnetic chaos healing and enhanced thermal content of the plasma. The helical structure extends on both sides of the vessel geometric axis, and is related to exceeding a threshold in the ratio between the amplitude of the dominant MHD mode and the amplitude of the secondary ones.