Credit assignment problems, for example policy evaluation in RL, often require bootstrapping prediction errors through preceding states or maintaining temporally extended memory traces; solutions which are unfavourable or implausible for biological networks of neurons. We propose theta sequences -- chains of neural activity during theta oscillations in the hippocampus, thought to represent rapid playthroughs of awake behviour -- as a solution. By analysing and simulating a model for theta sequences we show they compress behaviour such that existing but short O(10)ms neuronal memory traces are effectively extended allowing for bootstrap-free credit assignment without long memory traces, equivalent to the use of eligibility traces in TD(\lambda).