While the stress response represents an example of allostasis that enables the organism to cope with environmental and psychosocial challenges, its chronic activation imposes an allostatic load that contributes to the cumulative wear and tear of the system and induces negative mental and physical health outcomes. Nonetheless, the underlying basis of the stress-disease connection is still poorly understood and represents a gap in the knowledge that requires further research. We investigated the effects of chronic glucocorticoid stimulation in three independent human primary fibroblast lines, as an in vitro model of chronic psychosocial stress. By deploying a longitudinal, high-frequency, repeated-measures strategy across their entire lifespan, we were able to determine that chronically stressed cells present a significant increase in their total energy expenditure and that this stress-induced hypermetabolism is linked to an acceleration of their biological aging. Expanding from our results and placing emphasis on the energetic costs associated with the activation of the stress response, we proposed the “Energetic Model of Allostatic Load”. This model proposes that chronic stress causes a redirection of the energetic resources towards allostatic responses and away from growth, maintenance, and repair processes, which in turn leads to the accumulation of damage that will further contribute to the development of disease and increased risk of mortality. Finally, we highlighted new avenues to quantify allostatic load and its link to health via the integration of systemic and cellular energy expenditure measurements together with classic biomarkers, that could contribute to further advances in the stress field.