The maintenance of cooperative behavior is fundamental for the prosperity of human societies. Empirical studies show that high cooperation is frequently associated with the presence of strong social ties, but they are silent on whether a causal mechanism exists, how it operates, and what features of the social environment are conducive to its emergence. Here we show experimentally that strong ties increase cooperation and welfare by enabling the emergence of a close-knit and strongly bound cooperative elite. Crucially, this cooperative elite is more prevalent in social environments characterized by a large payoff difference between weak and strong ties, and no gradation in the process of strengthening a tie. These features allow cooperative individuals to adopt an all or nothing strategy to tie strengthening based on the well-known mechanism of direct reciprocity: participants become very selective by forming strong ties only with other cooperative individuals and severing ties with everyone else. Once formed, these strong ties are persistent and enhance cooperation. A dichotomous society emerges with cooperators prospering in a close-knit, strongly bound elite, and defectors earning low payoffs in a weakly connected periphery. Methodologically, our set-up provides a framework to investigate the role of the strength of ties in an experimental setting.