Microscopic, single crystals of sodium dodecylsulphate, Na⁺.C₁₂H₂₅O₄S^-, have been investigated by electron diffraction under conditions of carefully controlled temperature. The studies showed that the specimens are two-dimensional in the crystallographic sense and that a first-order solid-solid transition takes place at 283 K. The existence of the transition is shown by the discontinuous change of lattice parameters and the abrupt disappearance of all hk0 reflections with h + k odd at this temperature. Linear, thermal-expansion coefficients along the a and b directions are reported for the low-temperature form. The phenomenon is compared with similar transitions occurring in paraffins, and interpreted as the onset of rotational motions by the hydrocarbon chains of sodium dodecylsulphate about their longitudinal axes.