The problem of the conductivity of a thin conductive nanolayer is solved taking into account the quantum theory of transport processes. The layer thickness can be comparable to or less than the de Broglie wavelength of charge carriers. The constant-energy surface has the form of an ellipsoid of revolution with the main axis parallel to the layer plane. Analytical expressions are obtained for the conductivity tensor components as a function of dimensionless thickness, chemical potential, ellipticity parameter, and surface roughness parameters. The conductivity analysis for the limiting cases of a degenerate and non-degenerate electron gas are conducted. The results are compared with known experimental data for a silicon layer.