Drought causes massive crop quality and yield losses. Limiting the adverse effects of water deficits on crop yield is an urgent goal for a more sustainable agriculture. With this aim, six chicory varieties were subjected to drought conditions during seed germination and at the six week-old plant growth stage, in order to identify some morphological and/or molecular markers of drought resistance. Selvatica, Zuccherina di Trieste and Galatina varieties, with a high vegetative development, showed a major germination index, greater seedling development (6 days of growth) and a greater dehydration resistance (6 weeks of growth plus 10 days without water) than the other ones (Brindisina, Esportazione and Rossa Italiana). Due to the reported involvement, in the abiotic stress response, of xyloglucan endotransglucosylase/hydrolases (XTHs) and late embryogenesis abundant (LEA) multigene families, XTH29 and LEA4 expression profiles were investigated under stress conditions for all analyzed chicory varieties. We showed evidence that chicory varieties with high CiXTH29 and CiLEA4 basal expression and vegetative development levels better tolerate drought stress conditions than varieties that show overexpression of the two genes only in response to drought. Other specific morphological traits characterized almost all chicory varieties during dehydration, i.e., the appearance of lysigen cavities and a general increase of the amount of xyloglucans in the cell walls of bundle xylem vessels. Our results highlighted that high CiXTH29 and CiLEA4 basal expression, associated with a high level of vegetative growth, is a potential marker for drought stress tolerance.