We report a high-resolution synchrotron grazing incidence x-ray diffraction measurement of a surface crystalline monolayer at the liquid-vapor interface of the n-alkane eicosane (C20H42) just above its melting temperature. The peak width of the surface monolayer rotator phase is shown to be resolution limited and implies positional correlations of at least approximately 1 microm. The high resolution allowed determination of the temperature dependence of the peak position over the narrow (3 degrees C) temperature range of the surface crystal phase. The two-dimensional thermal expansion was determined to be (dA/dT)/A=1.8(+/-0.1)x10(-3) degrees C-1, which is comparable to the expansion in similar chain length bulk n-alkane rotator phases. Our data are consistent with the power-law shaped scattering tails expected from quasi-long-range order in two dimensions.