Nature abhors disorder and degeneracy at low temperature. Designing materials that confront this requirement can therefore lead to new states in which the degeneracy is lifted. Geometric magnetic frustration provides a means of creating the initial degeneracy when equal interactions from different atomic neighbours try to align moments in opposite directions. We have found a novel modulation along the U chains of UAu2 below 43 K, incommensurate with the crystal lattice, in which the magnitude of the ordered moments (rather than direction) is modulated. On further cooling below 18 K quantum critical behaviour is observed that exists to very low temperatures of 0.42 K. Such quantum critical behaviour occurring within an already ordered state is unprecedented and is thought to be brought about by the frustration. The proposal is to look at the excitations associated with this behaviour.