Liveness temporal properties state that something "good" eventually happens, e.g., every request is eventually granted. In Linear Temporal Logic (LTL), there is no a priori bound on the "wait time" for an eventuality to be fulfilled. That is, Fp asserts that p holds eventually, but there is no bound on the time when p will hold. This is troubling, as designers tend to interpret an eventuality Fp as an abstraction of a bounded eventuality Fkp, for an unknown k, and satisfaction of a liveness property is often not acceptable unless we can bound its wait time. We introduce here PLTL, an extension of LTL with the prompt-eventually operator Fb. A system S satisfies a PLTL formula p if there is some bound k on the wait time for all prompt-eventually subformulas of p in all computations of S. We study various problems related to PLTL, including realizability, model checking, and assume-guarantee model checking, and show that they can be solved by techniques that are quite close to the standard techniques for LTL.