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We compare limb darkening laws derived from 3D hydrodynamical modelatmospheres and 1D hydrostatic MARCS models for the host stars of the twotransiting exoplanet systems HD 209458 and HD 189733. The surface brightnessdistribution of the stellar disks is calculated using 3D LTE spectrum formationand opacity sampling. We test our predictions using least-squares fits of modellight curves to primary eclipses that were observed with the Hubble SpaceTelescope (HST).  The limb darkening law derived from the 3D model of HD 209458 between 2900 Aand 5700 A produces significantly better fits to the HST data, removingsystematic residuals that were previously observed for model light curves basedon 1D predictions. This difference arises mainly from the shallower meantemperature structure of the 3D model, which is a consequence of the explicitsimulation of surface granulation. In the case of HD 189733, the modelatmospheres produce practically equivalent limb darkening curves between 2900 Aand 5700 A, partly due to obstruction by spectral lines, and the data are notsufficient to distinguish between the light curves. We also analyze HSTobservations between 5350 A and 10500 A for this star; the 3D model leads to abetter fit compared to 1D predictions.  The significant improvement of fit quality for the HD 209458 systemdemonstrates the higher degree of realism of 3D models and the importance ofsurface granulation for the formation of the atmospheric radiation field oflate-type stars. This result agrees well with recent investigations of limbdarkening in the solar continuum and other observational tests. The case of HD189733 is no contradiction as the model light curves are less sensitive to thetemperature stratification of the atmosphere and the observed data in the 2900A - 5700 A region are not sufficient to distinguish more clearly between 3D and1D limb darkening.

Limb darkening laws for two exoplanet host stars derived from 3D stellar model atmospheres