[en] Estimates of the spatial resolution of a liquid argon ionization drift chamber are presented in the paper. The results obtained exhibit a possibility to construct a simple coordinate detector with a spatial resolution of σ_x = 20 μm and a two-track separation better than 1 mm, while good energy resolution characteristics for the LA detector are being conserved. The calculations were performed for an ionization cylindrical chamber with the cathode and anode diameter 4 cm and 0.1 mm, respectively. The fluctuations of ionization losses in thin samples and the noise jitter after shaping were taken into account in the analysis. (orig.)