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 \1> (differing form state \0> 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 \1> and \0> states, respectively.
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