In this paper we study the optimal forest conservation policy by a hyperbolically discounting society. Society comprises a series of non-overlapping imperfectly altruistic generations each represented by its own government. Under uncertainty about future pay-offs we determine, as solution of an intergenerational dynamic game, the optimal timing of irreversible harvest. Earlier harvest occurs and the option value attached to the forest clearing decision is eroded under both the assumptions of naïve and sophisticated belief about future time-preferences. This results in a bias toward the current generation gratification which affects the intergenerational allocation of benefits and costs from harvesting and conserving a natural forest.