We introduce a novel transition path (TPS) sampling scheme employing nested sampling. Analogous to how nested sampling explores the entire configurational phase space for atomistic systems, nested TPS samples the entire available trajectory space in one simulation. Thermodynamic and path observables can be constructed a posteriori for all temperatures simultaneously. We exploit this to compute the rate of rare processes at arbitrarily low temperature through the coupling to easily accessible rates at high temperature. We illustrate the method on several model systems.