The fast growing family of organic-inorganic hybrid compounds has recently been attracting increased attention owing to the remarkable functional properties (magnetic, multiferroic, optoelectronic, photovoltaic) displayed by some of its members. Here we show that these compounds can also have great potential in the until now unexplored field of solid-state cooling by presenting giant barocaloric effects near room temperature already under easily accessible pressures in the hybrid perovskite [TPrA][Mn(dca)3] (TPrA: tetrapropylammonium, dca: dicyanamide). Moreover, we propose that this will not be an isolated example for such an extraordinary behaviour as many other organic-inorganic hybrids (metal-organic frameworks and coordination polymers) exhibit the basic ingredients to display large caloric effects which can be very sensitive to pressure and other external stimuli. These findings open up new horizons and great opportunities for both organic-inorganic hybrids and for solid-state cooling technologies.