This paper investigates how people subdivided in social groups behave in an economy without property rights. Facing a linear production technology groups follow Markovian strategies for consumption and investment. Additionally, they may spend effort in an appropriation contest. For a symmetric society I show that conflict prevents investment and growth. In a society at peace economic growth may occur. Growth, however, is decreasing in the degree of social fractionalization and smaller than it could be under secure property rights. In an economy populated by social groups of unequal size an asymmetric equilibrium exists. A large majority may behave peacefully although continuously challenged by a predatory minority. In that case the economy either stagnates or grows at a low rate. Growth is decreasing in the size of the predatory minority and its conflict intensity.