In this paper we study the relationship between inequality and social instability. While the argument that inequality can be damaging for the cohesion of a society is old, the empirical evidence is rather mixed. We use a novel approach to tackle this question and isolate the concepts of inequality and instability in a laboratory experiment. In the experiment, two groups are interacting with each other repeatedly and have an incentive to cooperate even though cooperation comes at the cost of inter-group inequality. In the second half of the experiment, we vary the extent of the implied inequality. Our results show that increasing inequality has a destabilising effect, with the disadvantaged group beginning to attack the status quo. We show that this behaviour is consistent with a theoretical framework based on disadvantageous inequality aversion and myopic best response. Moreover, we find that certain characteristics, such as worsening the absolute situation of the disadvantaged group, or a sudden rather than a gradual increase in inequality aggravate the destabilising effect of inequality. Finally, we show that history matters, with people responding differently to the same level of inequality depending on their past experiences.