We demonstrate single-shot readout of quantum states of the Josephson charge qubit. The quantum bits are transformed into and stored as classical bits ~charge quanta! in a dynamic memory cell—a superconducting island. The transformation of state u1& ~differing form state u0& by an extra Cooper pair! is a result of a controllable quasiparticle tunneling to the island. The charge is then detected by a conventional single-electron transistor, electrostatically decoupled from the qubit. We study relaxation dynamics in the system and obtain the readout efficiency of 87% and 93% for u1& and u0& states, respectively.