We present a theoretical treatment of the ${\mathit{D}}_{\mathit{h}\mathit{d}}$ phase of a one-dimensional chiral discotic liquid crystal of ${\mathit{D}}_3$ symmetry molecules. This model is shown to reduce to a one-dimensional classical chiral planar model in a twofold anisotropy field. The thermodynamic properties and correlation functions are calculated numerically using the transfer-matrix method. Analytical results are obtained in the isotropic limit. The thermal expansion coefficient is shown to change sign at low temperature. The specific heat shows a crossover from the intrinsic planar character to an Ising-like behavior at low temperature.

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