The electricity required for air conditioning is soaring worldwide. Absorption chillers represent an alternative to classical vapor compression systems, using heat instead of electricity. However, absorption chillers powered by renewable geothermal heat have received little attention so far. This paper introduces a system using a hot geothermal fluid (typically in the range of 80–110 °C) to produce cooling through a single-effect absorption chiller, and Domestic Hot Water (DHW) through a heat exchanger. It considers a hotel located in Martinique, a French Caribbean island. The electric consumption of every subsystem has been thoroughly estimated. The originality of this paper is twice: i) the system is modelled in TRNSYS software considering dynamic conditions, ii) the system undergoes surrogate modelling and multi-objective optimization to minimize both the cost and the CO2 content of the delivered thermal energy. Several scenarios are considered, depending upon the geothermal temperature, mass flow rate, well remoteness, and demand size. The studied system appears to be systematically more expensive than a combination of a classical vapor compression chiller and a boiler for DHW. However, it can significantly decrease the CO2 content of the provided energy, especially in an island where most electricity is generated from fossil fuels. The proximity of the geothermal well and the use of the warm water leaving the absorption generator (here for DHW production) appear to be key factors for system relevance, along with a hotter geothermal fluid (e.g., 110 °C instead of 80 °C).