Political clientelism is a dyadic relation in which a politician (the patron) gives material goods and services to a citizen (the client), in exchange for political support. We argue that there is a two-way relation between clientelism and income inequality and poverty. In a poor society in which income inequality is high, clientelism will be a natural outcome. Once clientelism is established, it is harder for democracy to redistribute income and it is easier for the society to be caught in a poverty trap. We develop a two-part game-theoretic model. In the first part, clientelism emerges in a poor and unequal society as a consequence of social preferences, in particular, strong reciprocity. In the second part, using evolutionary and stochastic game theory, we show that clientelism causes income inequality and poverty.