We show that introducing rational inattention into a model with uninsurable unemployment risk can generate multiple steady states, when the same model with full information has a unique steady state. The model features heterogeneity and persistence in household labour market expectations, consistent with survey evidence. In a heterogeneous agent New Keynesian model, we find that rational inattention to the future hiring rate generates a high employment steady state with moderate inflation, and an unemployment trap with very low (but positive) inflation and a low job hiring rate.