A two-terminal capacitance method has been devised to measure the coefficient of linear thermal expansion ( alpha ) of thin films as conventional methods are unsuitable. The formula to evaluate the observed value of the thermal expansion coefficient ( alpha _obs) has been obtained and the relevant correction factor has been incorporated in the final formula alpha _true= alpha _obs+ alpha _el where alpha _el and alpha _true are the thermal expansion coefficients of electrode film and sample thin film respectively. The design of the dilatometric cell, the preparation of the thin-film specimen and the electrode film configuration are described. The change in capacitance with temperature of the vacuum capacitor, where the specimen film is the spacer, is used to evaluate alpha _obs. This technique has been standardised using thin platelets ( approximately 100 mu m) of a single crystal of NaCl. The other considerations which are important for the precision of this measurement technique are also discussed.