We introduce fractal social organizations—a novel class of socio-technical complex systems characterized by a distributed, bio-inspired, hierarchical architecture. Based on a same building block that is recursively applied at different layers, said systems provide a homogeneous way to model collective behaviors of different complexity and scale. Key concepts and principles are enunciated by means of a case study and a simple formalism. As preliminary evidence of the adequacy of the assumptions underlying our systems here, we define and study an algebraic model for a simple class of social organizations. We show how despite its generic formulation, geometric representations of said model exhibit the spontaneous emergence of complex hierarchical and modular patterns characterized by structured addition of complexity and fractal nature — which closely correspond to the distinctive architectural traits of our fractal social organizations. Some reflections on the significance of these results and a view to the next steps of our research conclude this contribution.