In Western Europe, future climate changes go hand-in-hand with increasing risks of droughts and heat waves during summer. For forest ecosystems, a drought may result in both an increase in tree mortality and a reduction in tree growth. These impacts are delayed over time, i.e., there is a time gap between the drought and its impacts on the forest stand, which makes it possible to adjust forest management practices and, in particular, to prematurely harvest the impacted stand and to replant a new one if it is economically profitable to do so. Consequently, we define Climate Services (CS) as the information that supports forest owners in their decision to prematurely harvest or not after a drought. Our paper aims at developing a method to estimate the economic value of these CS in the case of a maritime pine stand in Southwestern France. Using a comparison of Land Expected Values (LEV) over an infinite period of forest rotations, our analysis suggests that the Climate Service Value (CSV) is highly dependent on three characteristics: (1) the age of the forest exposed to the drought; (2) the intensity of the drought in terms of both mortality and growth impacts; and (3) the discount rate value used. Overall, for a 2% discount rate for a young stand (less than 15–20 years old), the CSV is rather low and ranges from 0 to €50/ha depending on the intensity of the drought. However, for a mature stand, the CSV rapidly increases, up to a maximum the year before the optimal harvest date. In this latter case, the CSV may be as high as €4900/ha for intense droughts.