We report on the very peculiar magnetic properties of an ensemble of very weakly coupled lithium-doped MoS2 nanotubes. The magnetic susceptibility chi of the system is nearly 3 orders of magnitude greater than in typical Pauli metals, yet there is no evidence for any instability which would alleviate this highly frustrated state. Instead, the material exhibits peculiar paramagnetic stability down to very low temperatures, with no evidence of a quantum critical point as T-->0 in spite of clear evidence for strongly correlated electron behavior. The exceptionally weak intertube interactions appear to lead to a realization of a near-ideal one-dimensional state in which fluctuations prevent the system from reordering magnetically or structurally.