Water is renowned for its anomalous behaviors, the majority of which can be linked to the distributed H-bond network of bulk water. Ultra-confinement of the water molecule can remove H-bonding leaving only molecular water. Such a condition exists in natural cordierite crystals, where water is trapped in a channel with a diameter of 5.7 Å, running through the center of the unit cell parallel to the c axis. We show that DSC reveals the existence of a 1-D glass linked to water in these channels. In these channels, water molecules in truncated, sparse 1-D strings can interact via dipole-dipole correlation only. Under these conditions a physical 1-D glass is formed from these strings. This highly unusual state can be explained by a modified Ising model, proposed by Semenov. This model predicts a dependence of the glass transition temperature, Tg, on the size of these domains. This is confirmed experimentally.